Cumulative Review 467 12. The mean room rate for two adults for a random sample of 26 three-star hotels in Cincinnati has a sample standard deviation of $31. Assume the population is normally distributed. (Adapted from Expedia) (a) Construct a 99% confidence interval for the population variance. (b) Construct a 99% confidence interval for the population standard deviation. (c) A travel analyst claims that the standard deviation of the mean room rate for two adults at three-star hotels in Cincinnati is at most $30. At a = 0.01, can you reject the travel analyst’s claim? Interpret the decision in the context of the original claim. 13. An education organization claims that the mean SAT scores for male athletes and male non-athletes at a college are different. A random sample of 26 male athletes at the college has a mean SAT score of 1189 and a standard deviation of 218. A random sample of 18 male non-athletes at the college has a mean SAT score of 1376 and a standard deviation of 186. At a = 0.05, can you support the organization’s claim? Interpret the decision in the context of the original claim. Assume the populations are normally distributed and the population variances are equal. 14. The annual earnings (in dollars) for 30 randomly selected locksmiths are shown below. Assume the population is normally distributed. (Adapted from Salary.com) 48,694 46,856 42,912 61,672 71,112 54,861 69,454 71,841 59,751 69,612 54,284 52,166 66,360 48,164 65,272 35,250 61,127 65,397 58,925 58,916 59,017 53,070 45,199 69,941 69,492 57,085 53,829 52,692 68,298 53,792 (a) Construct a 95% confidence interval for the population mean annual earnings for locksmiths. (b) A researcher claims that the mean annual earnings for locksmiths is $55,000. At a = 0.05, can you reject the researcher’s claim? Interpret the decision in the context of the original claim. 15. A medical research team studied the use of a marijuana extract to treat children with an epilepsy disorder. Of the 52 children who were given the extract, the number of convulsive seizures was reduced from 12 to 6 per month. Of the 56 children who were given a placebo, the number of convulsive seizures was reduced from 15 to 14 per month. At a = 0.10, can you support the claim that the proportion of monthly convulsive seizure reduction is greater for the group that received the extract than for the group that received the placebo? Interpret the decision in the context of the original claim. (Adapted from the New England Journal of Medicine) 16. A random sample of 40 ostrich eggs has a mean incubation period of 42 days. Assume the population standard deviation is 1.6 days. (a) Construct a 95% confidence interval for the population mean incubation period. (b) A zoologist claims that the mean incubation period for ostriches is at least 45 days. At a = 0.05, can you reject the zoologist’s claim? Interpret the decision in the context of the original claim. 17. A researcher claims that 5% of people who wear eyeglasses purchase their eyeglasses online. Describe type I and type II errors for a hypothesis test of the claim. (Source: Consumer Reports)
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