388 CHAPTER 8 Hypothesis Testing Statistical Literacy and Critical Thinking 1.Mean Wait Time at Space Mountain A formal hypothesis test is to be conducted to test the claim that the wait times at the Space Mountain ride in Walt Disney World have a mean equal to 40 minutes. a. What is the null hypothesis, and how is it denoted? b. What is the alternative hypothesis, and how is it denoted? c. What are the possible conclusions that can be made about the null hypothesis? d. Is it possible to conclude that “there is sufficient evidence to support the claim that the mean wait time is equal to 40 minutes”? 2.Estimates vs. Hypothesis Tests Labels on cans of Dr. Pepper soda indicate that they contain 12 oz of the drink. We could collect samples of those cans and accurately measure the actual contents, then we could use methods of Section 7-2 for making an estimate of the mean amount of Dr. Pepper in cans, or we could use those measured amounts to test the claim that the cans contain a mean of 12 oz. What is the difference between estimating the mean and testing a hypothesis about the mean? 3. Interpreting P-value The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of p 7 0.5, which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the method, which of the following P-values would you prefer as a result in your hypothesis test: 0.999, 0.5, 0.95, 0.05, 0.01, 0.001? Why? 4.Vitamin C vs. Lisinopril A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Merck pills with 40 mg of lisinopril that is used to treat high blood pressure. Identify which one of the following errors is most serious, explain why it is most serious, and characterize the error as being a type I error or a type II error. i. For lisinopril, fail to reject H0: m = 40 mg when the mean is actually different from 40 mg. ii. For lisinopril, reject H0: m = 40 mg when the mean is actually equal to 40 mg. iii. For vitamin C, fail to reject H0: m = 500 mg when the mean is actually different from 500 mg. iv. For vitamin C, reject H0: m = 500 mg when the mean is actually equal to 500 mg. Identifying H0 and H1. In Exercises 5–8, do the following: a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses. 5.Landline PhonesClaim: Fewer than 10% of homes have only a landline telephone and no wireless phone. Sample data: A survey by the National Center for Health Statistics showed that among 16,113 homes, 5.8% had landline phones without wireless phones. 6.Light Year Claim: Most adults know that a light year is a measure of distance. Sample data: A Pew Research Center survey of 3278 adults showed that 72% knew that a light year is a measure of distance. 7.Systolic Blood Pressure Claim: The mean systolic blood pressure of a healthy adult is less than 123 mm Hg. Sample data: Data Set 1 “Body Data” in Appendix B shows that for 300 healthy adults, the mean systolic blood pressure level is 122.96 mm Hg and the standard deviation is 15.85 mm Hg. 8-1 Basic Skills and Concepts
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