1) Three firms carry inventories that differ in size. Firm A's inventory contains 2000 items, firm B's inventory contains 5000 items, and firm C's inventory contains 10,000 items. The population standard deviation for the cost of the items in each firm's inventory is = 144. A statistical consultant recommends that each firm take a sample of 50 items from its inventory to provide statistically valid estimates of the average cost per item. Managers of the small firm state that because it has the smallest population, it should be able to make the estimate from a much smaller sample than that required by the larger firms. However, the consultant states that to obtain the same standard error and thus the same precision in the sample results, all firms should use the same sample size regardless of population size. a. Using the finite population correction factor, compute the standard error for each of the three firms given a sample of size 50. b. What is the probability that for each firm the sample mean will be within 25 of the population mean ? 2) Jupiter Media used a survey to determine how people use their free time. Watching television was the most popular activity selected by both men and women (The Wall Street Journal, January 26, 2004). The proportion of men and the proportion of women who selected watching television as their most popular leisure time activity can be estimated from the following sample data. Gender Men Women Sample Size 800 600 Watching TV 248 156 a. State the hypotheses that can be used to test for a difference between the proportion for the population of men and the proportion for the population of women who selected watching television as their most popular leisure time activity. b. What is the sample proportion of men who selected watching television as their most popular leisure time activity? What is the sample proportion of women? c. Conduct the hypothesis test and compute the p-value. At a .05 level of significance, what is your conclusion? d. What is the margin of error and 95% confidence interval estimate of the difference between the population proportions? 3) A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow. Hours Spent Studying Total Points Earned 45 40 30 35 90 75 60 65 105 90 65 50 90 90 80 80 55 45 75 65 a. Develop a 95% prediction interval for the total points earned by Mark Sweeney. 4) A sample of 9 days over the past six months showed that a dentist treated the following numbers of patients: 22, 25, 20, 18, 15, 22, 24, 19, and 26. If the number of patients seen per day is normally distributed, would an analysis of these sample data reject the hypothesis that the variance in the number of patients seen per day is equal to 10? Use a .10 level of significance. What is your conclusion? 5) Part variability is critical in the manufacturing of ball bearings. Large variances in the size of the ball bearings cause bearing failure and rapid wearout. Production standards call for a maximum variance of .0001 when the bearing sizes are measured in inches. A sample of 15 bearings shows a sample standard deviation of .014 inches. a. Use = .10 to determine whether the sample indicates that the maximum acceptable variance is being exceeded. b. Compute the 90% confidence interval estimate of the variance of the ball bearings in the population. 6) Is there any difference in the variability in golf scores for players on the LPGA Tour (the women's professional golf tour) and players on the PGATour (the men's professional golf tour)? A sample of 20 tournament scores from LPGA events showed a standard deviation of 2.4623 strokes, and a sample of 30 tournament scores from PGA events showed a standard deviation of 2.2118 (Golfweek, February 7, 2009, and March 7, 2009). Conduct a hypothesis test for equal population variances to determine if there is any statistically significant difference in the variability of golf scores for male and female professional golfers. Use = .10. What is your conclusion