Unformatted text preview: Ch. 11 Inferences on Two Samples 11.1 Inferences about Two Means: Dependent Samples
1 Distinguish between Independent and Dependent Sampling MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Classify the two given samples as independent or dependent. Sample 1: Pre training weights of 23 people Sample 2: Post  training weights of 23 people A) dependent B) independent 2) Classify the two given samples as independent or dependent. Sample 1: The weights in pounds of 26 newborn females Sample 2: The weights in pounds of 26 newborn males A) independent B) dependent 3) Classify the two given samples as independent or dependent. Sample 1: The scores of 16 students who took the ACT Sample 2: The scores of 16 different students who took the SAT A) independent B) dependent 4) If the individuals selected for a sample have no influence upon which individuals are selected for a second sample, then the samples are said to be A) Independent B) Dependent C) Inconsistent D) Consistent 5) Two samples are said to be dependent if A) The individuals in one sample are used to determine the individuals in a second sample. B) The individuals in one sample have no influence over the selection of the individuals in a second sample. C) Some individuals, but not all, in one sample exert influence over who is selected for inclusion in a second ample. D) Sampling for inclusion in the two samples is done with replacement. 2 Test Hypotheses Regarding Matched Pairs Data MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Data sets A and B are dependent. Find d. A 23 B 21 21 17 40 18 36 24 28 15 Assume that the paired data came from a population that is normally distributed. A) 9.0 B)  5.1 C) 33.1 D) 25.2 Page 250 2) Data sets A and B are dependent. Find d. A 6.7 B 9.1 7.7 8.0 9.6 7.9 6.6 6.7 7.8 9.2 Assume that the paired data came from a population that is normally distributed. A)  0.94 B)  0.76 C) 0.58 D) 0.89 3) Data sets A and B are dependent. Find sd. A 40 B 38 38 34 57 35 53 41 45 32 Assume that the paired data came from a population that is normally distributed. A) 7.8 B) 5.6 C) 6.8 D) 8.9 4) Data sets A and B are dependent. Find sd. A 6.9 B 9.3 7.9 8.2 9.8 8.1 6.8 6.9 8.0 9.4 Assume that the paired data came from a population that is normally distributed. A) 1.73 B) 1.21 C) 1.32 D) 1.89 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 5) Data sets A and B are dependent. Test the claim that μd =0. Use α = 0.05. A 11 B 9 9 5 28 6 24 12 16 3 Assume that the paired data came from a population that is normally distributed. 6) Data sets A and B are dependent. Test the claim that μd =0. Use α = 0.01. A 8.0 9.0 B 10.4 9.3 10.9 9.2 7.9 8.0 9.1 10.5 Assume that the paired data came from a population that is normally distributed. 7) Nine students took the SAT. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Test the claim that the test preparation had no effect on their scores. Use α = 0.05. Assume that the distribution is normally distributed. Student 1234567 8 9 Scores before course 720 860 850 880 860 710 850 1200 950 Scores after course 740 860 840 920 890 720 840 1240 970 Page 251 8) A weight lifting coach claims that weight lifters can increase their strength by taking a certain supplement. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed below. Thirty days later, after regular training using the supplement, they are tested again. The new results are listed below. Test the claim that the supplement is effective in increasing the athletesʹ strength. Use α = 0.05. Assume that the distribution is normally distributed. Athlete 1 2 3 4 5 6 7 8 9 Before 215 240 188 212 275 260 225 200 185 After 225 245 188 210 282 275 230 195 190 9) A pharmaceutical company wishes to test a new drug with the expectation of lowering cholesterol levels. Ten subjects are randomly selected and pretested. The results are listed below. The subjects were placed on the drug for a period of 6 months, after which their cholesterol levels were tested again. The results are listed below. (All units are milligrams per deciliter.) Test the companyʹs claim that the drug lowers cholesterol levels. Use α = 0.01. Assume that the distribution is normally distributed. Subject 1 2 3 4 5 6 7 8 9 10 Before 195 225 202 195 175 250 235 268 190 240 After 180 220 210 175 170 250 205 250 190 225 10) In a study of effectiveness of physical exercise on weight loss, 20 people were randomly selected to participate in a program for 30 days. Test the claim that exercise had no bearing on weight loss. Use α = 0.02. Assume that the distribution is normally distributed. Weight before Program 178 210 156 188 193 225 190 165 168 200 (in pounds) Weight after program 182 205 156 190 183 220 195 155 165 200 (in pounds) Weight before Program 186 172 166 184 225 145 208 214 148 174 (in pounds) Conʹt Weight after program 180 173 165 186 240 138 203 203 142 174 (in pounds) Conʹt 11) A local school district is concerned about the number of school days missed by its teachers due to illness. A random sample of 10 teachers is selected. The number of days absent in one year is listed below. An incentive program is offered in an attempt to decrease the number of days absent. The number of days absent in one year after the incentive program is listed below. Test the claim that the incentive program cuts down on the number of days missed by teachers. Use α = 0.05. Assume that the distribution is normally distributed. A B C D E F G H I J Teacher 87 2 94 2 075 Days absent before 3 incentive 1 77 0 82 0 155 Days absent after incentive Page 252 12) A physician claims that a personʹs diastolic blood pressure can be lowered if, instead of taking a drug, the person listens to a relaxation tape each evening. Ten subjects are randomly selected and pretested. Their blood pressures, measured in millimeters of mercury, are listed below. The 10 patients are given the tapes and told to listen to them each evening for one month. At the end of the month, their blood pressures are taken again. The data are listed below. Test the physicianʹs claim. Use α = 0.01. Patient 1 2 3 4 5 6 7 8 9 10 96 Before 85 96 92 83 80 91 79 98 93 82 90 92 75 74 80 82 88 89 80 After MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 13) When performing a hypothesis test upon two dependent samples, the variable of interest is A) The differences that exist between the matched  pair data B) All of the combined data C) The absolute value of the differences that exist between the matched  pair data D) The data that is the same in both samples 14) Robustness in hypothesis testing means A) Departures from normality do not adversely affect the results B) There are no departures from normality C) The data is effected by outliers D) All processes can be exactly duplicated by selecting another pair of samples 3 Construct and Interpret Confidence Intervals about the Population Mean Difference of Matched Pairs Data MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Construct a 95% confidence interval for data sets A and B. Data sets A and B are dependent. A 30 B 28 28 24 47 25 43 35 31 22 Assume that the paired data came from a population that is normally distributed. A) ( 0.696, 18.700) B) ( 1.324, 8.981) C) ( 0.113, 12.761) D) ( 15.341, 15.431) 2) Construct a 99% confidence interval for data sets A and B. Data sets A and B are dependent. A 5.8 B 8.2 6.8 7.1 8.7 7.0 5.7 6.9 5.8 8.3 Assume that the paired data came from a population that is normally distributed. A) ( 4.502, 2.622) B) ( 25.123, 5.761) C) ( 21.342, 18.982) D) ( 15.123, 15.123) Page 253 3) Nine students took the SAT. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Construct a 95% confidence interval for μd. Assume that the distribution is normally distributed. Student 1234567 8 9 Scores before course 720 860 850 880 860 710 850 1200 950 Scores after course 740 860 840 920 890 720 840 1240 970 A) ( 30.503,  0.617) B) ( 20.341, 4.852) C) ( 10.321, 15.436) D) (1.651, 30.590) 4) We are interested in comparing the average supermarket prices of two leading colas in the Tampa area. Our sample was taken by randomly going to each of eight supermarkets and recording the price of a six  pack of cola of each brand. The data are shown in the following table: Price Supermarket Brand 1 Brand 2 Difference 1 $2.25 $2.30 $  0.05 2 2.47 2.45 0.02 3 2.38 2.44  0.06 4 2.27 2.29  0.02 5 2.15 2.25  0.10 6 2.25 2.25 0.00 7 2.36 2.42  0.06 8 2.37 2.40  0.03 x1 = 2.3125 x2 = 2.3500 d =  0.0375 s1 = 0.1007 s2 = 0.0859 sd = 0.0381 Find a 98% confidence interval for the difference in mean price of brand 1 and brand 2. Assume that the paired data came from a population that is normally distributed. A) ( 0.0779, 0.0029) B) ( 0.1768, 0.1018) C) ( 0.0846, 0.0096) D) ( 0.0722,  0.0028) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 5) A new weight reducing technique, consisting of a liquid protein diet, is currently undergoing tests before its introduction into the market. A typical test performed is the following: The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let μ1 be the true mean weight of individuals before starting the diet and let μ2 be the true mean weight of individuals after 3 weeks on the diet. Person 1 2 3 4 5 Weight Before Diet 151 196 189 198 205 Weight After Diet 144 191 186 192 201 Summary information is as follows: d = 5, sd = 1.58. Calculate a 90% confidence interval for the difference between the mean weights before and after the diet is used. Assume that the paired data came from a population that is normally distributed. Page 254 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 6) Seven randomly selected plants that bottle the same beverage implemented a time management program in hopes of improving productivity. The average time, in minutes, that it took the companies to produce the same quantity of bottles before and after the program are listed below. Assume the two population distributions are normal. Plant 1 2 3 4 5 6 7 Before 75 89 31 90 120 50 40 After 70 80 30 85 100 49 42 Construct a 90% confidence interval for μd . Assume that the paired data came from a population that is normally distributed. A) (0.21, 10.93) B) (1.60, 9.54) C) ( 0.22, 11.36) D) ( 22, 33.3) 7) When forming a confidence interval for matched  pair data the point estimate is the A) Mean of the differences C) Standard deviation of the differences B) Difference of the means D) Differences of the standard deviations 11.2 Inference about Two Means: Independent Samples
1 Test Hypotheses Regarding the Difference of Two Independent Means MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the standardized test statistic, t, to test the claim that μ1 = μ2 . Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. n 1 = 25 n 2 = 30 x1 = 20 x2 = 18 s1 = 1.5 s2 = 1.9 A) 4.361 B) 3.287 C) 2.892 D) 1.986 2) Find the standardized test statistic, t, to test the claim that μ1 = μ2 . Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. n 1 = 14 n 2 = 12 x1 = 3 x2 = 4 s1 = 2.5 s2 = 2.8 A)  0.954 B)  0.915 C)  1.558 D)  0.909 3) Find the standardized test statistic, t, to test the claim that μ1 > μ2 . Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. n 1 = 18 n 2 = 13 x1 = 560 s1 = 40 A) 1.282 x2 = 545 s2 = 25 B) 3.271 Page 255 C) 2.819 D) 1.865 4) Find the standardized test statistic, t, to test the claim that μ1 < μ2 . Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. n 1 = 15 n 2 = 15 x2 = 28.91 x1 = 26.36 s1 = 2.9 s2 = 2.8 A)  2.450 B)  3.165 C)  1.667 D)  0.669 5) Find the standardized test statistic, t, to test the claim that μ1 ≠ μ2 . Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. n 1 = 11 n 2 = 18 x1 = 4.7 x2 = 5.1 s1 = 0.76 s2 = 0.51 A)  1.546 B)  1.821 C)  2.123 D)  1.326 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 6) Test the claim that μ1 = μ2 . Two samples are randomly selected from normal populations. The sample statistics are given below. n 1 = 25 n 2 = 30 x2 = 23 x1 = 25 s1 = 1.5 s2 = 1.9 7) Test the claim that μ1 = μ2 . Two samples are randomly selected from normal populations. The sample statistics are given below. n 1 = 14 n 2 = 12 x2 = 4 x1 = 3 s1 = 2.5 s2 = 2.8 8) Test the claim that μ1 > μ2 . Two samples are randomly selected from normal populations. The sample statistics are given below. n 1 = 18 n 2 = 13 x2 = 475 x1 = 490 s1 = 40 s2 = 25 9) Test the claim that μ1 < μ2 . Two samples are randomly selected from normal populations. The sample statistics are given below. n 1 = 15 n 2 = 15 x2 = 24.47 x1 = 21.92 s1 = 2.9 s2 = 2.8 Page 256 10) Test the claim that μ1 ≠ μ2 . Two samples are randomly selected from normal populations. The sample statistics are given below. n 1 = 11 n 2 = 18 x2 = 9.1 x1 = 8.7 s1 = 0.76 s2 = 0.51 11) A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitorʹs bank checks the waiting times at both banks. The sample statistics are listed below. Test the local bankʹs claim. Use α = 0.05. Local Bank Competitor Bank n 1 = 15 n 2 = 16 x1 = 5.3 minutes x2 = 5.6 minutes s1 = 1.1 minutes s2 = 1.0 minutes 12) A study was conducted to determine if the salaries of elementary school teachers from two neighboring districts were equal. A sample of 15 teachers from each district was randomly selected. The mean from the first district was $28,900 with a standard deviation of $2300. The mean from the second district was $30,300 with a standard deviation of $2100. Test the claim that the salaries from both districts are equal. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 13) Find the standardized test statistic to test the claim that μ1 = μ2 . Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.05. n 1 = 50 x1 = 23 s1 = 1.5 A) 6.2 n 2 = 60 x2 = 21 s2 = 1.9 B) 8.1 C) 4.2 D) 3.8 14) Find the standardized test statistic to test the claim that μ1 = μ2 . Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.05. n 1 = 40 n 2 = 35 x2 = 10 x1 = 9 s1 = 2.5 s2 = 2.8 A)  1.6 B)  0.8 C)  2.6 D)  1.0 15) Find the standardized test statistic to test the claim that μ1 > μ2 . Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.05. n 1 = 100 n 2 = 125 x2 = 690 x1 = 705 s1 = 45 s2 = 25 A) 2.98 B) 2.81 C) 1.86 D) 0.91 Page 257 16) Find the standardized test statistic to test the claim that μ1 < μ2 . Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.05. n 1 = 35 n 2 = 42 x2 = 30.92 x1 = 28.37 s1 = 2.9 s2 = 2.8 A)  3.90 B)  3.16 C)  2.63 D)  1.66 17) Find the standardized test statistic to test the claim that μ1 ≠ μ2 . Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.02. n 1 = 51 n 2 = 38 x1 = 2.3 x2 = 2.7 s1 = 0.76 s2 = 0.51 A)  2.97 B)  1.82 C)  2.12 D)  2.32 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 18) Test the claim that μ1 = μ2 . Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.05. n 1 = 50 n 2 = 60 x2 = 29 x1 = 31 s1 = 1.5 s2 = 1.9 19) Test the claim that μ1 > μ2 . Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.01. n 1 = 100 n 2 = 125 x2 = 430 x1 = 445 s1 = 45 s2 = 25 20) Test the claim that μ1 < μ2 . Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.05. n 1 = 35 n 2 = 42 x2 = 28.18 x1 = 25.63 s1 = 2.9 s2 = 2.8 21) Test the claim that μ1 ≠ μ2 . Two samples are randomly selected from each population. The sample statistics are given below. Use α = 0.02. n 1 = 51 n 2 = 38 x2 = 7.9 x1 = 7.5 s1 = 0.76 s2 = 0.51 Page 258 22) A study was conducted to determine if the salaries of elementary school teachers from two neighboring states were equal. A sample of 100 teachers from each state was randomly selected. The mean from the first state was $29,000 with a standard deviation of $2300. The mean from the second state was $30,400 with a standard deviation of $2100. Test the claim that the salaries from both states are equal. Use α = 0.05. 23) At a local college, 65 female students were randomly selected and it was found that their mean monthly income was $643 with a standard deviation of $121.50. Seventy  five male students were also randomly selected and their mean monthly income was found to be $685 with a standard deviation of $168.70. Test the claim that male students have a higher monthly income than female students. Use α = 0.01. 24) A medical researcher suspects that the pulse rate of smokers is higher than the pulse rate of non  smokers. Use the sample statistics below to test the researcherʹs suspicion. Use α = 0.05. Smokers n 1 = 100 x1 = 87 s1 = 4.8 Nonsmokers n 2 = 100 x2 = 84 s2 = 5.3 25) A statistics teacher believes that students in an evening statistics class score higher than the students in a day class. The results of a special exam are shown below. Can the teacher conclude that the evening students have a higher score? Use α = 0.01. Day Students n 1 = 36 x1 = 78 s1 = 5.8 Evening Students n 2 = 41 x2 = 81 s2 = 6.3 26) A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. The sample statistics are listed below. Test the local bankʹs claim. Use α = 0.05. Local Bank n 1 = 45 x1 = 4.4 minutes s1 = 1.1 minutes Competitor Bank n 2 = 50 x2 = 4.7 minutes s2 = 1.0 minute Page 259 27) A statistics teacher wanted to see whether there was a significant difference in ages between day students and night students. A random sample of 35 students is selected from each group. The data are given below. Test the claim that there is no difference in age between the two groups. Use α = 0.05. Day Students 22 24 24 23 19 19 23 22 18 21 21 18 18 25 29 24 23 22 22 21 20 20 20 27 17 19 18 21 20 23 26 30 25 21 25 Evening Students 18 23 25 23 21 21 23 24 27 31 24 20 20 23 19 25 24 27 23 20 20 21 25 24 23 28 20 19 23 24 20 27 21 29 30 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 28) What is the H0 for testing differences of the means of two independent samples? A) H0 : μ1  μ2 = 0 B) H0 : μ1 ≠ μ2 C) H0 : μ1 > μ2 D) H0 : μ1 < μ2 29) The degrees of freedom used when testing two independent samples where the population standard deviation is unknown is A) The smaller of n 1  1 or n 2  1 C) n 1 + n 2  2 B) The larger of n 1 ...
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