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Unformatted text preview: ST 560 Final Exam Summer 2009 Instructions: Use Minitab where possible to provide solutions to the following problems. All computer output should be incorporated into your answers. Do NOT supply computer output as part of an Appendix. Graphs should be no larger than half a page. Assume a significance level of α = 0.05 unless otherwise directed. A study investigating meat consumption in the U.S. is conducted. The researcher is interested in determining if the mean consumption of meat per person for 2007 is greater than the reported consumption of 62 lbs/person for the year 2002. Fifty (50) randomly selected volunteers record their meat consumption. The person’s yearly meat consumption and gender are recorded. The data are provided in the Excel data file named Final Exam 2009. 1. Construct boxplots of the variable Consumption for each gender and comment on the distributions of these two groups meat consumption. (6) 2. Construct normal probability plots for each gender’s meat consumption. Do the consumption values appear normally distributed? Why or why not? (6) 3. Test the hypothesis that meat consumption has increased since 2002. (12) a. Give the appropriate null and alternative hypotheses, test statistic, and p‐value associated with this hypothesis test. b. Provide the appropriate Minitab output. c. State your conclusion in the context of the problem. 4. The output provided in part (4) includes a p‐value. What is a p‐value? Hint: Do NOT tell me ‘if the p‐value is small reject the null hypothesis’. Define p‐value. (5) 5. A colleague notices the values of zero in the data set. He requests that the outliers be removed and the analysis redone. Do the data values (excluding zeroes) appear normally distributed? Why or why not? (5) 6. Repeat the test in part (3) on the modified data set and state the conclusions of the test. (8) Final Exam – Summer 2009 Page 1 7. 8. 9. Construct a power curve for the test in part (6) showing the power for the mean consumption values ranging from 60 to 66. What is the power of the test if the true mean consumption rate is 64 pounds? (Use the data with zero values omitted.) (8) Give a two‐sided 95% confidence interval for the mean consumption for the year 2007 excluding the zero values. (5) What is the margin of error associated with the confidence interval in problem 8? (5) 10. In problem 9, what sample size would be needed for a margin of error equal to 1.5 pounds? (5) 11. The second column in the data set indicates the subject’s gender (Male=1, Female=2). Find a 90% confidence interval for the difference in meat consumption for men and women. Justify the form of the interval used, i.e., whether you assume equal variances or not. (8) 12. Based on your confidence interval in part 11, would Ho: μ1 = μ2 be rejected? Why or why not?. (5) 13. Suppose 1% of the population in 2002 were vegetarians. Use the original data set to test the claim that the proportion of vegetarians has increased since 2002. (5) 14. A local chamber of commerce is backing a plan for a new convention center. The chamber states that 60 percent of the voters favor the plan, which would raise tourism business and taxes for the residents. Twenty of the registered voters in the community are called at random. Find the following: (8) a. Probability exactly 2 voters sampled favor the plan. b. Probability that no one says they favor the plan. c. On average , how many voters in twenty calls will favor the plan? Final Exam – Summer 2009 Page 2 16. A large men's store in a mall purchases suits from four different manufacturers in short, regular, and long. Their current selections are given in the contingency table below: Manufacturers Length HMS HF RL JC Total S 15 15 35 35 100 R 60 70 75 70 275 L 25 35 40 25 125 Total 100 120 150 130 500 Let the abbreviations and letters represent the events. For example Event S = a randomly selected suit is short event HMS = a randomly selected suit is manufactured by HMS. (9) a. Compute P(S). b. Compute P(S and HMS). c. Compute P(S  HMS). d. Compute P(HMS  S). Final Exam – Summer 2009 Page 3 ...
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