Review Exercises 339 Section 6.3 In Exercises 19–22, let p be the population proportion for the situation. (a) Find point estimates of p and q, (b) construct 90% and 95% confidence intervals for p, and (c) interpret the results of part (b) and compare the widths of the confidence intervals. 19. In a survey of 912 U.S. adults in Generation Z (born after 1996), 383 said they are at least somewhat likely to consider an electric vehicle for their next vehicle purchase. (Adapted from Pew Research Center) 20. In a survey of 13,749 U.S. adults, 5362 said they are at least somewhat likely to consider an electric vehicle for their next vehicle purchase. (Adapted from Pew Research Center) 21. In a survey of 73,901 college graduates, 23,991 obtained a postgraduate degree. (Adapted from Gallup) 22. In a survey of 2223 U.S. adults, 1334 say an occupation as an athlete is prestigious. (Adapted from The Harris Poll) 23. In Exercise 19, would it be unusual for the population proportion to be 38%? Explain. 24. In Exercise 22, would it be unusual for the population proportion to be 58%? Explain. 25. You wish to estimate, with 95% confidence, the population proportion of U.S. adults who have taken or planned to take a winter vacation in a recent year. Your estimate must be accurate within 5% of the population proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 32% of U.S. adults have taken or planned to take a winter vacation in a recent year. (Source: Rasmussen Reports) (c) Compare the results from parts (a) and (b). 26. In Exercise 25(b), would a sample size of 369 be acceptable? Explain. Section 6.4 In Exercises 27–30, find the critical values x 2 R and x 2 L for the level of confidence c and sample size n. 27. c = 0.95, n = 13 28. c = 0.98, n = 25 29. c = 0.90, n = 16 30. c = 0.99, n = 10 In Exercises 31 and 32, assume the sample is from a normally distributed population and construct the indicated confidence intervals for (a) the population variance s 2 and (b) the population standard deviation s. Interpret the results. 31. The number of field goals attempted by LeBron James in 13 randomly selected games of a recent NBA basketball season are listed. Use a 95% level of confidence. (Source: Basketball Reference) 26 13 25 22 13 15 16 20 15 13 26 23 20 32. The average weekly hours worked by service employees in the leisure and hospitality industry during a recent period of 31 months are listed. Use a 98% level of confidence. (Source: U.S. Bureau of Labor Statistics) 25.1 24.7 24.8 24.7 24.8 24.9 24.8 24.9 24.8 24.8 24.7 24.8 24.9 24.9 24.7 25.0 24.9 24.9 24.9 25.0 24.9 24.9 24.8 24.8 24.8 24.8 24.9 24.8 24.9 24.7 24.6
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