Chap012
102 Pages

Chap012

Course Number: GMGT 2340, Fall 2012

College/University: Utah Valley University

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Chapter 12 - Analysis of Variance Chapter 12 Analysis of Variance True / False Questions 1. The F distribution's curve is positively skewed. True False 2. One characteristic of the F distribution is that the computed F can only range between -1 and +1. True False 3. If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the null hypothesis. True False 4. For the hypothesis...

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12 Chapter - Analysis of Variance Chapter 12 Analysis of Variance True / False Questions 1. The F distribution's curve is positively skewed. True False 2. One characteristic of the F distribution is that the computed F can only range between -1 and +1. True False 3. If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the null hypothesis. True False 4. For the hypothesis test, , with n1 = 10 and n2 = 10, the F-test statistic is 2.56. At the 0.01 level of significance, we would reject the null hypothesis. True False 5. To employ ANOVA, the populations being studied must be approximately normally distributed. True False 6. To employ ANOVA, the populations should have approximately equal standard deviations. True False 12-1 Chapter 12 - Analysis of Variance 7. The alternative hypothesis used in ANOVA is True False . 8. For an ANOVA test, rejection of the null hypothesis does not identify which treatment means differ significantly. True False 9. In an ANOVA table, k represents the total number of sample observations and n represents the total number of treatments. True False 10. If a confidence interval for the difference between a pair of treatment means includes 0, then we reject the null hypothesis that there is no difference in the pair of treatment means. True False 11. If we want to determine which treatment means differ, we compute a confidence interval for the difference between each pair of means. True False 12. When a blocking effect is included in an ANOVA, the result is a larger error sum of squares. True False 13. When a blocking effect is included in an ANOVA, the analysis is more likely to detect differences in the treatment means. True False 12-2 Chapter 12 - Analysis of Variance 14. In a two-way ANOVA with interaction, there are two factor effects and an interaction effect. True False 15. Interaction between two factors occurs when the effect of one factor on the response variable is the same for any value of another factor. True False Multiple Choice Questions 16. An F statistic is: A. a ratio of two means. B. a ratio of two variances. C. the difference between three means. D. a population parameter. 17. What distribution does the F distribution approach as the sample size increases? A. Binomial B. Normal C. Poisson D. Exponential 18. Which statement is correct about the F distribution? A. Cannot be negative B. Cannot be positive C. Is the same as the t distribution D. Is the same as the z distribution 12-3 Chapter 12 - Analysis of Variance 19. Analysis of variance is used to A. compare nominal data. B. compute t test. C. compare population proportions. D. simultaneously compare several population means. 20. A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of three types of credit cards: MasterCard, Visa and Discover. Six MasterCard sales, seven Visa and five Discover sales were recorded. The store used an ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic? A. 18 in the numerator, 3 in the denominator B. 3 in the numerator, 18 in the denominator C. 2 in the numerator, 15 in the denominator D. 6 in the numerator, 15 in the denominator 21. Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline that will have the best fuel economy. The four grades are: regular, below regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades and the miles per gallon recorded. At the 0.05 level, what is the critical value of F used to test the hypothesis that the miles per gallon for each fuel is the same? A. 1.96 B. 4.07 C. 2.33 D. 12.00 12-4 Chapter 12 - Analysis of Variance 22. Three different fertilizers were applied to a field of celery. In computing F, how many degrees of freedom are there in the numerator? A. 0 B. 1 C. 2 D. 3 23. Suppose a package delivery company purchased 14 trucks at the same time. Five trucks were purchased from manufacturer A, four from manufacturer B, and five from manufacturer C. The cost of maintaining each truck was recorded. The company used ANOVA to test if the mean maintenance cost of the trucks from each manufacturer were equal. To apply the F test, how many degrees of freedom must be in the denominator? A. 2 B. 3 C. 11 D. 14 24. An experiment to determine the most effective way to teach safety principles applied four different teaching methods. Some employees were given programmed instruction booklets and worked through the course at their own pace. Other employees attended lectures. A third group watched a television presentation, and a fourth group was divided into small discussion groups. A high of 10 was possible. A sample of five tests was selected from each group. The test grade results were: At the 0.01 level, what is the critical value? A. 1.00 B. 1.96 C. 3.24 D. 5.29 12-5 Chapter 12 - Analysis of Variance 25. In ANOVA, an F statistic is used to test a null hypothesis such as: A. Option A B. Option B C. Option C D. Option D 26. An electronics company wants to compare the quality of their cell phones to the cell phones from three competitors. They sample 10 phones from each company and count the number of defects for each phone. If ANOVA were used to compare the average number of defects, then the treatments would be defined as: A. The number of cell phones sampled. B. The average number of defects. C. The total number of phones. D. The four companies. 27. Several employees have submitted different methods of assembling a subassembly. Sample data for each method are: How many treatments are there? A. 3 B. 4 C. 12 D. 0 12-6 Chapter 12 - Analysis of Variance 28. If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate? A. Too many degrees of freedom B. No difference between the population means C. A difference between at least one pair of population means D. All population means are different 29. A preliminary study of hourly wages paid to unskilled employees in three metropolitan areas was conducted. Seven employees were included from Area A, 9 from Area B, and 12 from Area C. The test statistic was computed to be 4.91. What can we conclude at the 0.05 level? A. Mean hourly wages of unskilled employees of all areas are equal B. Mean hourly wages in at least 2 metropolitan areas are different C. More degrees of freedom are needed D. None of these is correct 30. In ANOVA analysis, when the null hypothesis is rejected, we can test for differences between treatment means by A. constructing confidence intervals. B. adding another treatment. C. doing an additional ANOVA. D. doing a t test. 31. When the null hypothesis for an ANOVA analysis comparing four treatment means, is rejected, A. 2 comparisons of treatment means can be made. B. 4 comparisons of treatment means can be made. C. 6 comparisons of treatment means can be made. D. 8 comparisons of treatment means can be made. 12-7 Chapter 12 - Analysis of Variance 32. The null hypothesis for an ANOVA analysis comparing four treatment means is rejected. The four sample means are: 1= 10, 2=12, 3= 15, 4=18. The sample size for each treatment is the same. If ( 1) is significantly different from zero, then 2 A. 1 is significantly less than 2, 3, and 4. B. 2 is significantly less than 3 and 4. C. 3 and 4 are significantly different. D. 1, 2, 3, and 4 are all equal. 33. When testing for differences between treatment means, the t statistic is based on: A. The treatment degrees of freedom. B. The total degrees of freedom. C. The error degrees of freedom. D. The ratio of treatment and error degrees of freedom. 34. When testing for differences between treatment means, a confidence interval is based on A. the mean square error. B. the standard deviation. C. the sum of squared errors. D. the standard error of the mean. 35. When testing for differences between treatment means, the degrees of freedom for the t statistic are: A. k B. (n - 1) C. (n - k) D. (1/n1 + 1/n2) 12-8 Chapter 12 - Analysis of Variance 36. A manufacturer of automobile transmissions uses two different processes. Management ordered a study of the production costs to see if there is a difference among the two processes. A summary of the findings is shown below. What is the critical value of F at the 5% level of significance? A. 19.45 B. 3.00 C. 4.41 D. 4.38 37. A manufacturer of automobile transmissions uses two different processes. Management ordered a study of the production costs to see if there is a difference between the two processes. A summary of the findings is shown below. What is the critical value of F at the 1% level of significance? A. 9.46 B. 8.29 C. 8.18 D. 4.61 12-9 Chapter 12 - Analysis of Variance 38. A manufacturer of automobile transmissions uses three different processes. Management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the degrees of freedom for the treatment sum of squares? A. 2 B. 3 C. 10 D. 27 39. A manufacturer of automobile transmissions uses three different processes. Management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the degrees of freedom for the error sum of squares? A. 3 B. 10 C. 27 D. 30 12-10 Chapter 12 - Analysis of Variance 40. A manufacturer of automobile transmissions uses three different processes. Management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the total degrees of freedom? A. 27 B. 28 C. 29 D. 30 41. Given the following Analysis of Variance table for three treatments each with six observations. What are the degrees of freedom for the treatment and error sum of squares? A. 3 and 18 B. 2 and 17 C. 3 and 15 D. 2 and 15 42. Given the following Analysis of Variance table for three treatments each with six observations. What is the critical value of F at the 5% level of significance? A. 3.29 B. 3.68 C. 3.59 D. 3.20 12-11 Chapter 12 - Analysis of Variance 43. Given the following Analysis of Variance table for three treatments each with six observations. What is the mean square for treatments? A. 71.2 B. 71.4 C. 558 D. 534 44. Given the following Analysis of Variance table for three treatments each with six observations. What is the computed value of F? A. 7.48 B. 7.84 C. 8.84 D. 8.48 45. Given the following Analysis of Variance table for three treatments each with six observations. What is the decision regarding the null hypothesis? A. Reject H0 - there is a difference in treatment means B. Fail to reject H0 - there is a difference in treatment means C. Reject H0 - there is a difference in errors D. Fail to reject H0 - there is a difference in errors 12-12 Chapter 12 - Analysis of Variance 46. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What is H0? A. Option A B. Option B C. Option C D. Option D 47. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What is H1? A. Option A B. Option B C. Option C D. Option D 12-13 Chapter 12 - Analysis of Variance 48. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What are the degrees of freedom for the numerator of the F ratio? A. 8 B. 9 C. 10 D. 18 49. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What are the degrees of freedom for the denominator of the F ratio? A. 20 B. 18 C. 10 D. 9 50. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What is the critical value of F at the 0.01 level of significance? A. 5.85 B. 5.35 C. 6.51 D. 4.03 12-14 Chapter 12 - Analysis of Variance 51. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What is the critical value of F at the 0.05 level of significance? A. 5.85 B. 5.35 C. 3.18 D. 4.03 52. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: The calculated F ratio is A. 3.484 B. 1.867 C. 3.18 D. 5.35 53. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: At the 1% level of significance, what is the decision? A. Reject the null hypothesis and conclude the variances are different. B. Fail to reject the null hypothesis and conclude the variances are different. C. Reject the null hypothesis and conclude the variances are the same. D. Fail to reject the null hypothesis and conclude the variances are the same. 12-15 Chapter 12 - Analysis of Variance 54. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: At the 5% level of significance, what is the decision regarding the null hypothesis? A. Reject the null hypothesis and conclude the variances are different. B. Fail to reject the null hypothesis and conclude no significant difference in the variances. C. Reject the null hypothesis and conclude the variances are the same. D. Fail to reject the null hypothesis and conclude the variances are the same. 55. A random sample of 30 executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 243.7. The following table summarized the results: When comparing the mean annual incomes for executives with Undergraduate and Master's Degree or more, the following 95% confidence interval can be constructed: A. 2.0 2.052 * 6.51 B. 2.0 3.182 * 6.51 C. 2.0 2.052 * 42.46 D. 2.0 3.182 * 42.46 12-16 Chapter 12 - Analysis of Variance 56. A random sample of 30 executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 243.7. The following table summarized the results: Based on the comparison between the mean annual incomes for executives with Undergraduate and Master's Degree or more, A. A confidence interval shows that the mean annual incomes are not significantly different. B. The ANOVA results show that the mean annual incomes are significantly different. C. A confidence interval shows that the mean annual incomes are significantly different. D. The ANOVA results show that the mean annual incomes are not significantly different. 57. A random sample of 30 executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 243.7. The following table summarized the results: When comparing the mean annual incomes for executives with a High School education or less and Undergraduate Degree, the 95% confidence interval shows an interval of 11.7 to 42.7 for the difference. This result indicates that A. There is no significant difference between the two incomes. B. The interval contains a difference of zero. C. Executives with an Undergraduate Degree earn significantly more than executives with a High School education or less. D. Executives with an Undergraduate Degree earn significantly less than executives with a High School education or less. 12-17 Chapter 12 - Analysis of Variance 58. A random sample of 40 companies with assets over $10 million was selected and asked for their annual computer technology expense and industry. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 195. The following table summarized the results: When comparing the mean annual computer technology expense for companies in the Education and Tax services industries, the following 95% confidence interval can be constructed: A. 13.5 2.026 * 5.78 B. 13.5 2.021 * 5.78 C. 13.5 2.026 * 13.96 D. 13.5 2.021 * 13.96 59. A random sample of 40 companies with assets over $10 million was selected and asked for their annual computer technology expense and industry. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 195. The following table summarized the results: Based on the comparison between the mean annual computer technology expense for companies in the Education and Tax services industries, A. A confidence interval shows that the mean annual computer technology expenses are not significantly different. B. The ANOVA results show that the mean annual computer technology expenses are significantly different. C. A confidence interval shows that the mean annual computer technology expenses are significantly different. D. The ANOVA results show that the mean annual computer technology expenses are not significantly different. 12-18 Chapter 12 - Analysis of Variance 60. A random sample of 40 companies with assets over $10 million was selected and asked for their annual computer technology expense and industry. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 195. The following table summarized the results: Based on the comparison between the mean annual computer technology expense for companies in the Tax Service and Food Service industries, the 95% confidence interval shows an interval of -14.85 to 5.85 for the difference. This result indicates that A. There is no significant difference between the two expenses. B. The interval contains a difference of 20.7. C. Companies in the Tax Service industry spend significantly less than companies in the Food Service industry. D. Companies in the Food Service industry spend significantly less than companies in the Tax Service industry. 61. A random sample of 16 companies was selected and asked for their annual dividend rate in three different industries: utilities, banking, and insurance. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 3.36. The following table summarized the results: When comparing the mean annual dividend rate for companies in the utilities and insurance industries, the following 95% confidence interval can be constructed: A. 5.78 2.160 * 2.40 B. 5.78 2.120 * 2.40 C. 5.78 2.160 * 1.11 D. 5.78 2.120 * 1.11 12-19 Chapter 12 - Analysis of Variance 62. A random sample of 16 companies was selected and asked for their annual dividend rate in three different industries: utilities, banking, and insurance. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 3.36. The following table summarized the results: Based on the comparison between the mean annual dividend rate for companies in the utilities and insurance industries, A. A confidence interval shows that the mean annual dividend rates are not significantly different. B. The ANOVA results show that the mean annual dividend rates are significantly different. C. A confidence interval shows that the mean annual dividend rates are significantly different. D. The ANOVA results show that the mean annual dividend rates are not significantly different. 63. A random sample of 16 companies was selected and asked for their annual dividend rate in three different industries: utilities, banking, and insurance. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 3.36. The following table summarized the results: Based on the comparison between the mean annual dividend rate for companies in the utilities and banking, the 95% confidence interval shows an interval of 1.28 to 6.28 for the difference. This result indicates that A. There is no significant difference between the two rates. B. The interval contains a difference of 5.00. C. The annual dividend rate in the utilities industry is significantly less than the annual dividend rate in banking industry. D. The annual dividend rate in banking industry is significantly less than the annual dividend rate in utilities industry. 12-20 Chapter 12 - Analysis of Variance 64. In a two-way ANOVA, a blocking variable is used to A. increase the error sum of squares. B. decrease the error sum of squares. C. increase the treatment sum of squares. D. decrease the treatment sum of squares. 65. In a two-way ANOVA, the sources of variation are A. Total variation and error variation. B. Total variation, treatment variation, and error variation. C. Total variation, treatment variation, blocking variation and error variation. D. Treatment variation and blocking variation. 66. The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow. What is the blocking variable? A. Day. B. Class time. C. Tuesday. D. 8:00 am class. 12-21 Chapter 12 - Analysis of Variance 67. The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow. What is the treatment variable? A. Day. B. Class time. C. Tuesday. D. 8:00 am class. 68. The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow. What are the block and treatment degrees of freedom? A. 5 and 3. B. 5 and 5. C. 4 and 2. D. 3 and 15. 12-22 Chapter 12 - Analysis of Variance 69. The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow. What is the critical F statistic for testing the hypothesis of equal treatment means at the 0.05 significance level? A. 1.96. B. 6.94. C. 3.84. D. 4.46. 70. In a two-way ANOVA with interaction, a significant interaction term indicates that A. the response variable is interactive. B. a blocking factor is present. C. both factors are unrelated. D. both factors have a combined effect on the response variable. 71. A two-way ANOVA with interaction has how many sources of variation? A. 5. B. 4. C. 3. D. 2. 72. If there are 5 levels of Factor A and 7 levels of Factor B for an ANOVA with interaction, what are the interaction degrees of freedom? A. 12. B. 35. C. 24. D. 10. 12-23 Chapter 12 - Analysis of Variance 73. The college of business was interested in comparing the interaction of Academic status and class time on class attendance. Three different classes were sampled for each cell in the table. The means for each cell follow. What are the total degrees of freedom? A. 44. B. 14. C. 4. D. 2. 74. The college of business was interested in comparing the interaction of Academic status and class time on class attendance. Three different classes were sampled for each cell in the table. The means for each cell follow. What are the error degrees of freedom? A. 44. B. 14. C. 30. D. 2. 12-24 Chapter 12 - Analysis of Variance 75. The college of business was interested in comparing the interaction of Academic status and class time on class attendance. Three different classes were sampled for each cell in the table. The means for each cell follow. What are the interaction degrees of freedom? A. 10. B. 2. C. 4. D. 8. Fill in the Blank Questions 76. The F distribution is a ______________ distribution. ________________________________________ 77. What is the shape of the F distribution? ______________________ ________________________________________ 78. What are the minimum and maximum of values of an F distribution? _______ and _______ ________________________________________ 79. All values in an F distribution must be _____________. ________________________________________ 12-25 Chapter 12 - Analysis of Variance 80. What test statistic is used to compare two variances? ________________ ________________________________________ 81. The F-distribution is useful when testing a requirement of two-sample tests of hypothesis. What is the assumption? ________________ ________________________________________ 82. ANOVA requires that the populations should be ______, ______, and _____. ________________________________________ 83. What statistical technique is used to test the equality of three or more population means? ____________________ ________________________________________ 84. What is the least number of sources of variation in ANOVA? _________ ________________________________________ 85. In an one-way ANOVA, what are the degrees of freedom associated with the error sum of squares? ___________ ________________________________________ 86. In an one-way ANOVA, how many degrees of freedom are associated with the numerator of the F ratio? _______ ________________________________________ 87. What is the sum of squares divided by its corresponding degrees of freedom called? _________________ ________________________________________ 12-26 Chapter 12 - Analysis of Variance 88. Assuming that the larger of two variances is in the numerator of an F statistic, in which tail of the F distribution is the rejection region for analysis of variance? ________ ________________________________________ 89. In ANOVA, when we do not reject the null hypothesis, what inference do we make about the population means? ________________ ________________________________________ 90. What is the null hypothesis for an ANOVA comparing three population means? ____________________ ________________________________________ 91. When H0 is rejected in ANOVA, _______ _______ are constructed to identify pairs of means that differ. ________________________________________ 92. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. What are the degrees of freedom for the numerator? ______ ________________________________________ 93. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. What are the degrees of freedom for the denominator? ______ ________________________________________ 94. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. If the sum of squares for the brands is 0.07, what is the mean square for brands? ______ ________________________________________ 12-27 Chapter 12 - Analysis of Variance 95. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. If the sum of squares for the error is 0.09, what is the mean square for the error? ______ ________________________________________ 96. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. What is the F critical value for = 0.05? ______ ________________________________________ 97. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. What is the calculated value of F, if the brand sum of squares is 0.07 and the error sum of squares is 0.09? ______ ________________________________________ 98. In a two-way ANOVA table with interaction, what are the error degrees of freedom? _________ ________________________________________ 99. When a second source of variance is included in the ANOVA analysis without interaction, that source is called a _________________. ________________________________________ 100. How many mean square errors are summarized in a two-way ANOVA table? _________ ________________________________________ 12-28 Chapter 12 - Analysis of Variance Short Answer Questions 101. A company compared the variance of salaries for employees who have been employed for 5 years or less with employees who have been employed for 10 years or more. They randomly selected 21 employees with 5 years or less experience and 15 employees with 10 years or more experience. The standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for the group with 10 years or more experience is $1,875. What is the F test statistic for the hypothesis test? 102. A company compared the variance of salaries for employees who have been employed for 5 years or less with employees who have been employed for 10 years or more. They randomly selected 21 employees with 5 years or less experience and 15 employees with 10 years or more experience. The standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for the group with 10 years or more experience is $1,875. Using the 0.05 significance level, what is the F critical value for the hypothesis test? 12-29 Chapter 12 - Analysis of Variance 103. A company compared the variance of salaries for employees who have been employed for 5 years or less with employees who have been employed for 10 years or more. They randomly selected 21 employees with 5 years or less experience and 15 employees with 10 years or more experience. The standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for the group with 10 years or more experience is $1,875. Using the 0.05 significance level, what is the decision regarding the null hypothesis? 104. To test the hypothesis that two population variances are equal, a random sample of size 13 was selected from the first population, and a random sample of size 21 was selected from the second population. What are the degrees of freedom to test the hypothesis? 105. To test the hypothesis that two population variances are equal, a random sample of size 13 was selected from the first population, and a random sample of size 21 was selected from the second population. Given that the sample standard deviation from the first population is larger than the sample standard deviation from the second population, what is the F-critical value using 0.01 as the significance level? 12-30 Chapter 12 - Analysis of Variance 106. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. The ANOVA table follows. What are the degrees of freedom for the machines? 107. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What are the degrees of freedom for the operators? 12-31 Chapter 12 - Analysis of Variance 108. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What are the degrees of freedom for the errors? 12-32 Chapter 12 - Analysis of Variance 109. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the critical value of F for the machine treatment effect at the 1% level of significance? ____ 110. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the critical value of F for the operator block effect at the 1% level of significance? 12-33 Chapter 12 - Analysis of Variance 111. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the mean square for machines? 112. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the mean square for operators? 12-34 Chapter 12 - Analysis of Variance 113. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the mean square for error? 114. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the computed value of F for the machines? 12-35 Chapter 12 - Analysis of Variance 115. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the computed value of F for the operators? _____ 116. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. Test the hypothesis that all operators are equally productive. State your decision in terms of the null hypothesis. 12-36 Chapter 12 - Analysis of Variance 117. An ANOVA showed the following comparison of four treatment means. Which treatment means are significantly different? 118. An ANOVA comparing the waiting times for four different emergency rooms shows the following comparison of the four mean waiting times. Which two pairs of means are significantly different? 12-37 Chapter 12 - Analysis of Variance 119. A random sample of 20 female executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 250. The following table summarized the results: To compare the mean annual incomes of female executives with an undergraduate degree and female executives with a high school or less education, compute the 95% confidence interval. 120. A random sample of 20 female executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 250. The following table summarized the results: To compare the mean annual incomes of female executives with an undergraduate degree and female executives with a Master's degree or more, compute the 99% confidence interval. 12-38 Chapter 12 - Analysis of Variance 121. A random sample of 20 female executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 250. The following table summarized the results: To compare the mean annual incomes of female executives with a high school education or less and female executives with a Master's degree or more, compute the 90% confidence interval. 122. The human resources department of a software company encourages their employees to participate in a wellness program. They sampled 16 employees, 2 males and 2 females from four different workout routines and measured their peak heart rate. The ANOVA for the research follows. What is the Interaction sum of squares? 12-39 Chapter 12 - Analysis of Variance 123. The human resources department of a software company encourages their employees to participate in a wellness program. They sampled 16 employees, 2 males and 2 females from four different workout routines and measured their peak heart rate. The ANOVA for the research follows. What is the Workout mean square? 124. The human resources department of a software company encourages their employees to participate in a wellness program. They sampled 16 employees, 2 males and 2 females from four different workout routines and measured their peak heart rate. The ANOVA for the research follows. What is the F-statistic for Gender? 12-40 Chapter 12 - Analysis of Variance 125. The human resources department of a software company encourages their employees to participate in a wellness program. They sampled 16 employees, 2 males and 2 females from four different workout routines and measured their peak heart rate. The ANOVA for the research follows. Which source of variation significantly affects peak heart rate? Essay Questions 126. What is the purpose of using a blocking variable in a two-way ANOVA? 127. When testing a hypothesis regarding the equality of two population means, what is the analogy to a blocking variable? 12-41 Chapter 12 - Analysis of Variance 128. In a two-way ANOVA, when is an interaction source of variance included? 129. What is the advantage of using ANOVA to test for differences among treatment means rather than testing all possible pairs of treatment means? 12-42 Chapter 12 - Analysis of Variance Chapter 12 Analysis of Variance Answer Key True / False Questions 1. The F distribution's curve is positively skewed. TRUE AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table. Topic: F-distribution 2. One characteristic of the F distribution is that the computed F can only range between -1 and +1. FALSE AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Easy Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table. Topic: F-distribution 3. If the computed value of F is 0.99 and the critical value is 3.89, we would not reject the null hypothesis. TRUE AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 12-43 Chapter 12 - Analysis of Variance 4. For the hypothesis test, , with n1 = 10 and n2 = 10, the F-test statistic is 2.56. At the 0.01 level of significance, we would reject the null hypothesis. FALSE AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 5. To employ ANOVA, the populations being studied must be approximately normally distributed. TRUE AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Easy Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means. Topic: ANOVA Concepts 12-44 Chapter 12 - Analysis of Variance 6. To employ ANOVA, the populations should have approximately equal standard deviations. TRUE AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Easy Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means. Topic: ANOVA Concepts 7. The alternative hypothesis used in ANOVA is FALSE . AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis. Topic: ANOVA Hypotheses 8. For an ANOVA test, rejection of the null hypothesis does not identify which treatment means differ significantly. TRUE AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis. Topic: ANOVA Hypotheses 9. In an ANOVA table, k represents the total number of sample observations and n represents the total number of treatments. FALSE AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-45 Chapter 12 - Analysis of Variance 10. If a confidence interval for the difference between a pair of treatment means includes 0, then we reject the null hypothesis that there is no difference in the pair of treatment means. FALSE AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 11. If we want to determine which treatment means differ, we compute a confidence interval for the difference between each pair of means. TRUE AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Easy Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12. When a blocking effect is included in an ANOVA, the result is a larger error sum of squares. FALSE AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 13. When a blocking effect is included in an ANOVA, the analysis is more likely to detect differences in the treatment means. TRUE AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Hard Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-46 Chapter 12 - Analysis of Variance 14. In a two-way ANOVA with interaction, there are two factor effects and an interaction effect. TRUE AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Easy Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 15. Interaction between two factors occurs when the effect of one factor on the response variable is the same for any value of another factor. FALSE AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Hard Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction Multiple Choice Questions 16. An F statistic is: A. a ratio of two means. B. a ratio of two variances. C. the difference between three means. D. a population parameter. AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Easy Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table. Topic: F-distribution 12-47 Chapter 12 - Analysis of Variance 17. What distribution does the F distribution approach as the sample size increases? A. Binomial B. Normal C. Poisson D. Exponential AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table. Topic: F-distribution 18. Which statement is correct about the F distribution? A. Cannot be negative B. Cannot be positive C. Is the same as the t distribution D. Is the same as the z distribution AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table. Topic: F-distribution 19. Analysis of variance is used to A. compare nominal data. B. compute t test. C. compare population proportions. D. simultaneously compare several population means. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means. Topic: ANOVA Concepts 12-48 Chapter 12 - Analysis of Variance 20. A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of three types of credit cards: MasterCard, Visa and Discover. Six MasterCard sales, seven Visa and five Discover sales were recorded. The store used an ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic? A. 18 in the numerator, 3 in the denominator B. 3 in the numerator, 18 in the denominator C. 2 in the numerator, 15 in the denominator D. 6 in the numerator, 15 in the denominator AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 21. Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline that will have the best fuel economy. The four grades are: regular, below regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades and the miles per gallon recorded. At the 0.05 level, what is the critical value of F used to test the hypothesis that the miles per gallon for each fuel is the same? A. 1.96 B. 4.07 C. 2.33 D. 12.00 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-49 Chapter 12 - Analysis of Variance 22. Three different fertilizers were applied to a field of celery. In computing F, how many degrees of freedom are there in the numerator? A. 0 B. 1 C. 2 D. 3 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 23. Suppose a package delivery company purchased 14 trucks at the same time. Five trucks were purchased from manufacturer A, four from manufacturer B, and five from manufacturer C. The cost of maintaining each truck was recorded. The company used ANOVA to test if the mean maintenance cost of the trucks from each manufacturer were equal. To apply the F test, how many degrees of freedom must be in the denominator? A. 2 B. 3 C. 11 D. 14 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-50 Chapter 12 - Analysis of Variance 24. An experiment to determine the most effective way to teach safety principles applied four different teaching methods. Some employees were given programmed instruction booklets and worked through the course at their own pace. Other employees attended lectures. A third group watched a television presentation, and a fourth group was divided into small discussion groups. A high of 10 was possible. A sample of five tests was selected from each group. The test grade results were: At the 0.01 level, what is the critical value? A. 1.00 B. 1.96 C. 3.24 D. 5.29 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-51 Chapter 12 - Analysis of Variance 25. In ANOVA, an F statistic is used to test a null hypothesis such as: A. Option A B. Option B C. Option C D. Option D AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Easy Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 26. An electronics company wants to compare the quality of their cell phones to the cell phones from three competitors. They sample 10 phones from each company and count the number of defects for each phone. If ANOVA were used to compare the average number of defects, then the treatments would be defined as: A. The number of cell phones sampled. B. The average number of defects. C. The total number of phones. D. The four companies. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Easy Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis. Topic: ANOVA Hypotheses 12-52 Chapter 12 - Analysis of Variance 27. Several employees have submitted different methods of assembling a subassembly. Sample data for each method are: How many treatments are there? A. 3 B. 4 C. 12 D. 0 AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis. Topic: ANOVA Hypotheses 28. If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate? A. Too many degrees of freedom B. No difference between the population means C. A difference between at least one pair of population means D. All population means are different AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-53 Chapter 12 - Analysis of Variance 29. A preliminary study of hourly wages paid to unskilled employees in three metropolitan areas was conducted. Seven employees were included from Area A, 9 from Area B, and 12 from Area C. The test statistic was computed to be 4.91. What can we conclude at the 0.05 level? A. Mean hourly wages of unskilled employees of all areas are equal B. Mean hourly wages in at least 2 metropolitan areas are different C. More degrees of freedom are needed D. None of these is correct AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 30. In ANOVA analysis, when the null hypothesis is rejected, we can test for differences between treatment means by A. constructing confidence intervals. B. adding another treatment. C. doing an additional ANOVA. D. doing a t test. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 31. When the null hypothesis for an ANOVA analysis comparing four treatment means, is rejected, A. 2 comparisons of treatment means can be made. B. 4 comparisons of treatment means can be made. C. 6 comparisons of treatment means can be made. D. 8 comparisons of treatment means can be made. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-54 Chapter 12 - Analysis of Variance 32. The null hypothesis for an ANOVA analysis comparing four treatment means is rejected. The four sample means are: 1= 10, 2=12, 3= 15, 4=18. The sample size for each treatment is the same. If ( 1) is significantly different from zero, then 2 A. 1 is significantly less than 2, 3, and 4. B. 2 is significantly less than 3 and 4. C. 3 and 4 are significantly different. D. 1, 2, 3, and 4 are all equal. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 33. When testing for differences between treatment means, the t statistic is based on: A. The treatment degrees of freedom. B. The total degrees of freedom. C. The error degrees of freedom. D. The ratio of treatment and error degrees of freedom. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: about Inferences pairs of treatment means 34. When testing for differences between treatment means, a confidence interval is based on A. the mean square error. B. the standard deviation. C. the sum of squared errors. D. the standard error of the mean. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-55 Chapter 12 - Analysis of Variance 35. When testing for differences between treatment means, the degrees of freedom for the t statistic are: A. k B. (n - 1) C. (n - k) D. (1/n1 + 1/n2) AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 36. A manufacturer of automobile transmissions uses two different processes. Management ordered a study of the production costs to see if there is a difference among the two processes. A summary of the findings is shown below. What is the critical value of F at the 5% level of significance? A. 19.45 B. 3.00 C. 4.41 D. 4.38 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-56 Chapter 12 - Analysis of Variance 37. A manufacturer of automobile transmissions uses two different processes. Management ordered a study of the production costs to see if there is a difference between the two processes. A summary of the findings is shown below. What is the critical value of F at the 1% level of significance? A. 9.46 B. 8.29 C. 8.18 D. 4.61 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 38. A manufacturer of automobile transmissions uses three different processes. Management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the degrees of freedom for the treatment sum of squares? A. 2 B. 3 C. 10 D. 27 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-57 Chapter 12 - Analysis of Variance 39. A manufacturer of automobile transmissions uses three different processes. Management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the degrees of freedom for the error sum of squares? A. 3 B. 10 C. 27 D. 30 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 40. A manufacturer of automobile transmissions uses three different processes. Management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below. What are the total degrees of freedom? A. 27 B. 28 C. 29 D. 30 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-58 Chapter 12 - Analysis of Variance 41. Given the following Analysis of Variance table for three treatments each with six observations. What are the degrees of freedom for the treatment and error sum of squares? A. 3 and 18 B. 2 and 17 C. 3 and 15 D. 2 and 15 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 42. Given the following Analysis of Variance table for three treatments each with six observations. What is the critical value of F at the 5% level of significance? A. 3.29 B. 3.68 C. 3.59 D. 3.20 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-59 Chapter 12 - Analysis of Variance 43. Given the following Analysis of Variance table for three treatments each with six observations. What is the mean square for treatments? A. 71.2 B. 71.4 C. 558 D. 534 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 44. Given the following Analysis of Variance table for three treatments each with six observations. What is the computed value of F? A. 7.48 B. 7.84 C. 8.84 D. 8.48 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-60 Chapter 12 - Analysis of Variance 45. Given the following Analysis of Variance table for three treatments each with six observations. What is the decision regarding the null hypothesis? A. Reject H0 - there is a difference in treatment means B. Fail to reject H0 - there is a difference in treatment means C. Reject H0 - there is a difference in errors D. Fail to reject H0 - there is a difference in errors AACSB: Reflective Thinking Bloom's: Analysis Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 46. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What is H0? A. Option A B. Option B C. Option C D. Option D AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 12-61 Chapter 12 - Analysis of Variance 47. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What is H1? A. Option A B. Option B C. Option C D. Option D AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 48. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What are the degrees of freedom for the numerator of the F ratio? A. 8 B. 9 C. 10 D. 18 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 12-62 Chapter 12 - Analysis of Variance 49. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What are the degrees of freedom for the denominator of the F ratio? A. 20 B. 18 C. 10 D. 9 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 50. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What is the critical value of F at the 0.01 level of significance? A. 5.85 B. 5.35 C. 6.51 D. 4.03 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 12-63 Chapter 12 - Analysis of Variance 51. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: What is the critical value of F at the 0.05 level of significance? A. 5.85 B. 5.35 C. 3.18 D. 4.03 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 52. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: The calculated F ratio is A. 3.484 B. 1.867 C. 3.18 D. 5.35 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 12-64 Chapter 12 - Analysis of Variance 53. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: At the 1% level of significance, what is the decision? A. Reject the null hypothesis and conclude the variances are different. B. Fail to reject the null hypothesis and conclude the variances are different. C. Reject the null hypothesis and conclude the variances are the same. D. Fail to reject the null hypothesis and conclude the variances are the same. AACSB: Reflective Thinking Skills Bloom's: Analysis Difficulty: Hard Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 54. Two accounting professors decided to compare the variance of their grading procedures. To accomplish this, they each graded the same 10 exams with the following results: At the 5% level of significance, what is the decision regarding the null hypothesis? A. Reject the null hypothesis and conclude the variances are different. B. Fail to reject the null hypothesis and conclude no significant difference in the variances. C. Reject the null hypothesis and conclude the variances are the same. D. Fail to reject the null hypothesis and conclude the variances are the same. AACSB: Reflective Thinking Bloom's: Analysis Difficulty: Hard Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 12-65 Chapter 12 - Analysis of Variance 55. A random sample of 30 executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 243.7. The following table summarized the results: When comparing the mean annual incomes for executives with Undergraduate and Master's Degree or more, the following 95% confidence interval can be constructed: A. 2.0 2.052 * 6.51 B. 2.0 3.182 * 6.51 C. 2.0 2.052 * 42.46 D. 2.0 3.182 * 42.46 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 56. A random sample of 30 executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 243.7. The following table summarized the results: Based on the comparison between the mean annual incomes for executives with Undergraduate and Master's Degree or more, A. A confidence interval shows that the mean annual incomes are not significantly different. B. The ANOVA results show that the mean annual incomes are significantly different. C. A confidence interval shows that the mean annual incomes are significantly different. D. The ANOVA results show that the mean annual incomes are not significantly different. AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-66 Chapter 12 - Analysis of Variance 57. A random sample of 30 executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 243.7. The following table summarized the results: When comparing the mean annual incomes for executives with a High School education or less and Undergraduate Degree, the 95% confidence interval shows an interval of 11.7 to 42.7 for the difference. This result indicates that A. There is no significant difference between the two incomes. B. The interval contains a difference of zero. C. Executives with an Undergraduate Degree earn significantly more than executives with a High School education or less. D. Executives with an Undergraduate Degree earn significantly less than executives with a High School education or less. AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-67 Chapter 12 - Analysis of Variance 58. A random sample of 40 companies with assets over $10 million was selected and asked for their annual computer technology expense and industry. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 195. The following table summarized the results: When comparing the mean annual computer technology expense for companies in the Education and Tax services industries, the following 95% confidence interval can be constructed: A. 13.5 2.026 * 5.78 B. 13.5 2.021 * 5.78 C. 13.5 2.026 * 13.96 D. 13.5 2.021 * 13.96 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-68 Chapter 12 - Analysis of Variance 59. A random sample of 40 companies with assets over $10 million was selected and asked for their annual computer technology expense and industry. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 195. The following table summarized the results: Based on the comparison between the mean annual computer technology expense for companies in the Education and Tax services industries, A. A confidence interval shows that the mean annual computer technology expenses are not significantly different. B. The ANOVA results show that the mean annual computer technology expenses are significantly different. C. A confidence interval shows that the mean annual computer technology expenses are significantly different. D. The ANOVA results show that the mean annual computer technology expenses are not significantly different. AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-69 Chapter 12 - Analysis of Variance 60. A random sample of 40 companies with assets over $10 million was selected and asked for their annual computer technology expense and industry. The ANOVA comparing the average computer technology expense among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 195. The following table summarized the results: Based on the comparison between the mean annual computer technology expense for companies in the Tax Service and Food Service industries, the 95% confidence interval shows an interval of -14.85 to 5.85 for the difference. This result indicates that A. There is no significant difference between the two expenses. B. The interval contains a difference of 20.7. C. Companies in the Tax Service industry spend significantly less than companies in the Food Service industry. D. Companies in the Food Service industry spend significantly less than companies in the Tax Service industry. AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-70 Chapter 12 - Analysis of Variance 61. A random sample of 16 companies was selected and asked for their annual dividend rate in three different industries: utilities, banking, and insurance. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 3.36. The following table summarized the results: When comparing the mean annual dividend rate for companies in the utilities and insurance industries, the following 95% confidence interval can be constructed: A. 5.78 2.160 * 2.40 B. 5.78 2.120 * 2.40 C. 5.78 2.160 * 1.11 D. 5.78 2.120 * 1.11 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-71 Chapter 12 - Analysis of Variance 62. A random sample of 16 companies was selected and asked for their annual dividend rate in three different industries: utilities, banking, and insurance. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 3.36. The following table summarized the results: Based on the comparison between the mean annual dividend rate for companies in the utilities and insurance industries, A. A confidence interval shows that the mean annual dividend rates are not significantly different. B. The ANOVA results show that the mean annual dividend rates are significantly different. C. A confidence interval shows that the mean annual dividend rates are significantly different. D. The ANOVA results show that the mean annual dividend rates are not significantly different. AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-72 Chapter 12 - Analysis of Variance 63. A random sample of 16 companies was selected and asked for their annual dividend rate in three different industries: utilities, banking, and insurance. The ANOVA comparing the mean annual dividend rate among three industries rejected the null hypothesis. The Mean Square Error (MSE) was 3.36. The following table summarized the results: Based on the comparison between the mean annual dividend rate for companies in the utilities and banking, the 95% confidence interval shows an interval of 1.28 to 6.28 for the difference. This result indicates that A. There is no significant difference between the two rates. B. The interval contains a difference of 5.00. C. The annual dividend rate in the utilities industry is significantly less than the annual dividend rate in banking industry. D. The annual dividend rate in banking industry is significantly less than the annual dividend rate in utilities industry. AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 64. In a two-way ANOVA, a blocking variable is used to A. increase the error sum of squares. B. decrease the error sum of squares. C. increase the treatment sum of squares. D. decrease the treatment sum of squares. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-73 Chapter 12 - Analysis of Variance 65. In a two-way ANOVA, the sources of variation are A. Total variation and error variation. B. Total variation, treatment variation, and error variation. C. Total variation, treatment variation, blocking variation and error variation. D. Treatment variation and blocking variation. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 66. The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow. What is the blocking variable? A. Day. B. Class time. C. Tuesday. D. 8:00 am class. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-74 Chapter 12 - Analysis of Variance 67. The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow. What is the treatment variable? A. Day. B. Class time. C. Tuesday. D. 8:00 am class. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-75 Chapter 12 - Analysis of Variance 68. The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow. What are the block and treatment degrees of freedom? A. 5 and 3. B. 5 and 5. C. 4 and 2. D. 3 and 15. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-76 Chapter 12 - Analysis of Variance 69. The college of business was interested in comparing the attendance for three different class times for a business statistics class. The data follow. What is the critical F statistic for testing the hypothesis of equal treatment means at the 0.05 significance level? A. 1.96. B. 6.94. C. 3.84. D. 4.46. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 70. In a two-way ANOVA with interaction, a significant interaction term indicates that A. the response variable is interactive. B. a blocking factor is present. C. both factors are unrelated. D. both factors have a combined effect on the response variable. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 12-77 Chapter 12 - Analysis of Variance 71. A two-way ANOVA with interaction has how many sources of variation? A. 5. B. 4. C. 3. D. 2. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 72. If there are 5 levels of Factor A and 7 levels of Factor B for an ANOVA with interaction, what are the interaction degrees of freedom? A. 12. B. 35. C. 24. D. 10. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 12-78 Chapter 12 - Analysis of Variance 73. The college of business was interested in comparing the interaction of Academic status and class time on class attendance. Three different classes were sampled for each cell in the table. The means for each cell follow. What are the total degrees of freedom? A. 44. B. 14. C. 4. D. 2. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 12-79 Chapter 12 - Analysis of Variance 74. The college of business was interested in comparing the interaction of Academic status and class time on class attendance. Three different classes were sampled for each cell in the table. The means for each cell follow. What are the error degrees of freedom? A. 44. B. 14. C. 30. D. 2. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 12-80 Chapter 12 - Analysis of Variance 75. The college of business was interested in comparing the interaction of Academic status and class time on class attendance. Three different classes were sampled for each cell in the table. The means for each cell follow. What are the interaction degrees of freedom? A. 10. B. 2. C. 4. D. 8. AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction Fill in the Blank Questions 76. The F distribution is a ______________ distribution. continuous AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table. Topic: F-distribution 12-81 Chapter 12 - Analysis of Variance 77. What is the shape of the F distribution? ______________________ Positively skewed AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table. Topic: F-distribution 78. What are the minimum and maximum of values of an F distribution? _______ and _______ Zero and positive infinity AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table. Topic: F-distribution 79. All values in an F distribution must be _____________. positive values AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-01 List the characteristics of the F distribution and locate values in an F table. Topic: F-distribution 80. What test statistic is used to compare two variances? ________________ F statistic AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Easy Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 12-82 Chapter 12 - Analysis of Variance 81. The F-distribution is useful when testing a requirement of two-sample tests of hypothesis. What is the assumption? ________________ The population variances are equal AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 82. ANOVA requires that the populations should be ______, ______, and _____. normal or normally distributed; independent; have equal standard deviations or variances AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means. Topic: ANOVA Concepts 83. What statistical technique is used to test the equality of three or more population means? ____________________ Analysis of variance (ANOVA) AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Easy Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means. Topic: ANOVA Concepts 84. What is the least number of sources of variation in ANOVA? _________ Two, treatment and error AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means. Topic: ANOVA Concepts 12-83 Chapter 12 - Analysis of Variance 85. In an one-way ANOVA, what are the degrees of freedom associated with the error sum of squares? ___________ n-k AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 86. In an one-way ANOVA, how many degrees of freedom are associated with the numerator of the F ratio? _______ k-1 AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 87. What is the sum of squares divided by its corresponding degrees of freedom called? _________________ Mean square AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 88. Assuming that the larger of two variances is in the numerator of an F statistic, in which tail of the F distribution is the rejection region for analysis of variance? ________ Upper AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-84 Chapter 12 - Analysis of Variance 89. In ANOVA, when we do not reject the null hypothesis, what inference do we make about the population means? ________________ They are equal AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis. Topic: ANOVA Hypotheses 90. What is the null hypothesis for an ANOVA comparing three population means? ____________________ Ho: 1 = 2 = 3 AACSB: Communication Abilities Bloom's: Knowledge Difficulty: Medium Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis. Topic: ANOVA Hypotheses 91. When H0 is rejected in ANOVA, _______ _______ are constructed to identify pairs of means that differ. confidence intervals AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 92. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. What are the degrees of freedom for the numerator? ______ 2 AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-85 Chapter 12 - Analysis of Variance 93. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. What are the degrees of freedom for the denominator? ______ 12 AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 94. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. If the sum of squares for the brands is 0.07, what is the mean square for brands? ______ 0.035 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 95. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. If the sum of squares for the error is 0.09, what is the mean square for the error? ______ 0.0075 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 12-86 Chapter 12 - Analysis of Variance 96. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. What is the F critical value for = 0.05? ______ 3.89 AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-04 Organize data into appropriate ANOVA tables for analysis. Topic: ANOVA Hypotheses 97. In a study of protein breakfast bars, five bars from each of three brands were tested to see if the mean amount of protein per bar differs among the brands. What is the calculated value of F, if the brand sum of squares is 0.07 and the error sum of squares is 0.09? ______ 4.66 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-05 Conduct a test of hypothesis among three or more treatment means and describe the results. Topic: The ANOVA test 98. In a two-way ANOVA table with interaction, what are the error degrees of freedom? _________ (n - kb) AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Hard Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 99. When a second source of variance is included in the ANOVA analysis without interaction, that source is called a _________________. blocking variable AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-87 Chapter 12 - Analysis of Variance 100. How many mean square errors are summarized in a two-way ANOVA table? _________ Three - treatment, block and error AACSB: Communication Abilities Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA Short Answer Questions 101. A company compared the variance of salaries for employees who have been employed for 5 years or less with employees who have been employed for 10 years or more. They randomly selected 21 employees with 5 years or less experience and 15 employees with 10 years or more experience. The standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for the group with 10 years or more experience is $1,875. What is the F test statistic for the hypothesis test? 1.408 AACSB: Analytic Skills Bloom's: Application Difficulty: Easy Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 102. A company compared the variance of salaries for employees who have been employed for 5 years or less with employees who have been employed for 10 years or more. They randomly selected 21 employees with 5 years or less experience and 15 employees with 10 years or more experience. The standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for the group with 10 years or more experience is $1,875. Using the 0.05 significance level, what is the F critical value for the hypothesis test? 2.39 AACSB: Analytic Skills Bloom's: Application Difficulty: Easy Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 12-88 Chapter 12 - Analysis of Variance 103. A company compared the variance of salaries for employees who have been employed for 5 years or less with employees who have been employed for 10 years or more. They randomly selected 21 employees with 5 years or less experience and 15 employees with 10 years or more experience. The standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for the group with 10 years or more experience is $1,875. Using the 0.05 significance level, what is the decision regarding the null hypothesis? Fail to reject the null hypothesis that the two population variances are equal. AACSB: Analytic Skills Bloom's: Application Difficulty: Easy Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 104. To test the hypothesis that two population variances are equal, a random sample of size 13 was selected from the first population, and a random sample of size 21 was selected from the second population. What are the degrees of freedom to test the hypothesis? 12 and 20 AACSB: Analytic Skills Bloom's: Application Difficulty: Easy Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 105. To test the hypothesis that two population variances are equal, a random sample of size 13 was selected from the first population, and a random sample of size 21 was selected from the second population. Given that the sample standard deviation from the first population is larger than the sample standard deviation from the second population, what is the F-critical value using 0.01 as the significance level? 3.23 AACSB: Analytic Skills Bloom's: Application Difficulty: Easy Learning Objective: 12-02 Perform a test of hypothesis to determine whether the variances of two populations are equal. Topic: Comparing two population variances 12-89 Chapter 12 - Analysis of Variance 106. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. The ANOVA table follows. What are the degrees of freedom for the machines? 3 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 107. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What are the degrees of freedom for the operators? 5 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-90 Chapter 12 - Analysis of Variance 108. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What are the degrees of freedom for the errors? 15 AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 109. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the critical value of F for the machine treatment effect at the 1% level of significance? ____ 5.42 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-91 Chapter 12 - Analysis of Variance 110. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the critical value of F for the operator block effect at the 1% level of significance? 4.56 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 111. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the mean square for machines? 38 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-92 Chapter 12 - Analysis of Variance 112. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the mean square for operators? 43 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 113. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the mean square for error? 3.6 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-93 Chapter 12 - Analysis of Variance 114. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the computed value of F for the machines? 10.56 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 115. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. What is the computed value of F for the operators? _____ 11.94 AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 12-94 Chapter 12 - Analysis of Variance 116. A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. ANOVA table follows. Test the hypothesis that all operators are equally productive. State your decision in terms of the null hypothesis. Reject the null hypothesis and conclude that the operators are not equally productive AACSB: Analytic Skills Bloom's: Application Difficulty: Medium Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 117. An ANOVA showed the following comparison of four treatment means. Which treatment means are significantly different? None AACSB: Reflective Thinking Bloom's: Analysis Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-95 Chapter 12 - Analysis of Variance 118. An ANOVA comparing the waiting times for four different emergency rooms shows the following comparison of the four mean waiting times. Which two pairs of means are significantly different? The mean waiting time for ER1 is significantly different from mean waiting time for ER2; The mean waiting time for ER2 is significantly different from mean waiting time for ER4; AACSB: Reflective Thinking Bloom's: Analysis Difficulty: Medium Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 119. A random sample of 20 female executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 250. The following table summarized the results: To compare the mean annual incomes of female executives with an undergraduate degree and female executives with a high school or less education, compute the 95% confidence interval. [21.46, 64.54] AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-96 Chapter 12 - Analysis of Variance 120. A random sample of 20 female executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 250. The following table summarized the results: To compare the mean annual incomes of female executives with an undergraduate degree and female executives with a Master's degree or more, compute the 99% confidence interval. [-18.66, 28.66] AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-97 Chapter 12 - Analysis of Variance 121. A random sample of 20 female executives from companies with assets over $1 million was selected and asked for their annual income and level of education. The ANOVA comparing the average income among three levels of education rejected the null hypothesis. The Mean Square Error (MSE) was 250. The following table summarized the results: To compare the mean annual incomes of female executives with a high school education or less and female executives with a Master's degree or more, compute the 90% confidence interval. [31.72, 64.28] AACSB: Analytic Skills Bloom's: Application Difficulty: Hard Learning Objective: 12-06 Develop confidence intervals for the differences between treatment means and interpret the results. Topic: Inferences about pairs of treatment means 12-98 Chapter 12 - Analysis of Variance 122. The human resources department of a software company encourages their employees to participate in a wellness program. They sampled 16 employees, 2 males and 2 females from four different workout routines and measured their peak heart rate. The ANOVA for the research follows. What is the Interaction sum of squares? 60.187 AACSB: Analytic Skills Bloom's: Analysis Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 123. The human resources department of a software company encourages their employees to participate in a wellness program. They sampled 16 employees, 2 males and 2 females from four different workout routines and measured their peak heart rate. The ANOVA for the research follows. What is the Workout mean square? 189.063 AACSB: Analytic Skills Bloom's: Analysis Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 12-99 Chapter 12 - Analysis of Variance 124. The human resources department of a software company encourages their employees to participate in a wellness program. They sampled 16 employees, 2 males and 2 females from four different workout routines and measured their peak heart rate. The ANOVA for the research follows. What is the F-statistic for Gender? 1.94 AACSB: Analytic Skills Bloom's: Analysis Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 125. The human resources department of a software company encourages their employees to participate in a wellness program. They sampled 16 employees, 2 males and 2 females from four different workout routines and measured their peak heart rate. The ANOVA for the research follows. Which source of variation significantly affects peak heart rate? Workout routine AACSB: Analytic Skills Bloom's: Analysis Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 12-100 Chapter 12 - Analysis of Variance Essay Questions 126. What is the purpose of using a blocking variable in a two-way ANOVA? A blocking variable accounts for an additional source of variation. The total sum of squares is now partitioned into treatment, block and error sum of squares. By including a blocking variable in an ANOVA, the error sum of squares and the corresponding mean square error (MSE) is decreased. The ultimate effect is in the calculation of the F-statistic to test the hypothesis of equal treatment means. Since the MSE has been decreased by the inclusion of a blocking variable, the hypothesis test of equal treatment means will be more sensitive to significant differences because the denominator of the F-statistic is smaller. AACSB: Reflective Thinking Bloom's: Analysis Difficulty: Hard Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 127. When testing a hypothesis regarding the equality of two population means, what is the analogy to a blocking variable? The pairing of observations. AACSB: Reflective Thinking Bloom's: Analysis Difficulty: Hard Learning Objective: 12-07 Carry out a test of hypothesis among treatment means using a blocking variable and understand the results. Topic: Two-way ANOVA 128. In a two-way ANOVA, when is an interaction source of variance included? An interaction source of variance is included in an ANOVA if there is reason to believe that the variance in the response variable is affected by both factors in a two-way ANOVA. AACSB: Reflective Thinking Bloom's: Comprehension Difficulty: Medium Learning Objective: 12-08 Perform a two-way ANOVA with interaction and describe the results. Topic: Two-way ANOVA with interaction 12-101 Chapter 12 - Analysis of Variance 129. What is the advantage of using ANOVA to test for differences among treatment means rather than testing all possible pairs of treatment means? The advantage of using ANOVA rather than comparing all possible pairs of treatment means is to avoid the buildup of Type I error. For example, if three independent means were compared using an alpha of 0.05, there would be three independent tests. The probability of not making a Type I error is 0.95. The probability of not making a Type I error on the three independent tests is 0.95*0.95*0.95 or 0.86. Now the cumulative probability of a Type I error is 0.14 rather than 0.05. ANOVA simultaneously compares all possible means at a stated level of significance or Type I error rate. AACSB: Reflective Thinking Bloom's: Comprehension Difficulty: Hard Learning Objective: 12-03 Describe the ANOVA approach for testing differences in sample means. Topic: ANOVA Concepts 12-102
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