1 Determine the lower- and upper-tail critical values of 2 for each of the following two-tail tests: 1) = 0.01, n = 24 2) = 0.05, n = 20 3) = 0.10, n = 16 Question 2 Marketers know that tastes differ in various regions of country. In the rental car business, an industry expert has given the opinion that there are strong regional preferences for the size of car. He quotes the following data in support of his view: Preferred Car Type Northeast Southeast Northwest Southwest Total Full Size 105 120 105 70 400 Intermediate 120 100 130 150 500 All others Total 25 250 30 250 15 250 30 250 100 1000 a) State the appropriate null and alternative hypothesis b) Do the data support the expert's opinion at 0.05 significance level? Question 3 The director of transportation of a large company is interested in the usage of the company's van pool program. She surveyed 129 of her employees on the usage of the program before and after a campaign to convince her employees to use the service and obtained the following results Before Use After Do Not Use Total Use 27 44 71 Do Not Use 33 25 58 Total 60 69 129 She will use this information to perform test using a level of significance of 0.05. The director now wants to know if the proportion of employees who use the service before the campaign and the proportion of employees who use the service after the campaign are the same. a) Which test should she use? b) What should she conclude? (show your work) Question 4 More shoppers do the majority of their grocery shopping on Saturday than any other day of the week. However, is there a difference in the various age groups in the proportion of people who do the majority of their grocery shopping on Saturday? A study showed the results for the different age groups (extracted from "Major Shopping by Day," Progressive Grocer Annual Report, April 30, 2002). The data were reported as percentages, and no sample sizes were given: Assume that 200 shoppers for each age category were surveyed. 1) Is there evidence of a significant difference among the age groups with respect to major grocery shopping day? (Use = 0.05.) 2) Determine the p-value in (1) and interpret its meaning. 3) If appropriate, use the Marascuilo procedure and = 0.05 to determine which age groups are different. Discuss your results. 4) Discuss the managerial implications of (1) and (3). That is, how can grocery stores use this information to improve marketing and sales? Be specific. Question 5 A manufacturer of doorknobs has a production process that is designed to provide a doorknob with a target diameter of 2.5 inches. In the past, the standard deviation of the diameter has been 0.035 inch. In an effort to reduce the variation in the process, various studies have resulted in a redesigned process. A sample of 25 doorknobs produced under the new process indicates a sample standard deviation of 0.025 inch. 1) At the 0.05 level of significance, is there evidence that the population standard deviation is less than 0.035 inch in the new process? 2) What assumption do you need to make in order to perform this test? 3) Compute the p-value in part (a) and interpret its meaning