Instructions: Below you will nd questions and sample data. Please use the provided data to complete the tasks and to answer the questions. 1. A hat company states that the mean hat size for a male is at least 7125. A random sample of 32 hat sizes has a mean of 115 and a standard deviation of 0.35. a. At Cf. = 0.05, can you reject the company's claim that the mean hat size for a male is at least 125? Be sure to state the pvalue for this test. b. In the context of the problem, describe what a Type I error and a Type II error would mean. 2. The mean ACT score for 43 male high school students is 21.1 and the standard deviation is 5.0. The mean ACT score for 56 female high school students is 20.9 and the standard deviation is 4]. At the 1% signicance level, can you reject the claim that male and female high school students have equal ACT score averages? Be sure to use the ovalue to make your conclusion. 3. A medical research team conducted a study to test the effect of a migraine drug. 01' the 400 subjects who took the drug, 100 were pain free after two hours. Of the 40? subjects that took a placebo, 40 were pain free after two hours. Can you reject the claim that the proportion of subjects who are painfree is the same for the two groups? Use the appropriate hypothesis test at the 2% significance level. Be sure to use the p~value to make your conclusion. 4. The Federal Bureau of Prisons publishes data in Prison Statistics on the times served by prisoners released from federal institutions for the rst time. Independent random samples of released prisoners in the fraud and rearms offense categories yielded the following information on time served, in months. At the 5% signicance level, do the data provide sufcient evidence to conclude that the mean time served for fraud is less than that for rearms offenses? Dataset: Fraud Firearm 9.2 18. 9 9.6 16.6 10.5 22.1 10.? 19.4 10.2 20 11.5 21.4 12.3 12.5 12.2 13.4 13.9 19.5 9.9 10.8