434 CHAPTER 8 Hypothesis Testing 8. Distributions Using the methods of this chapter, identify the distribution that should be used for testing a claim about the given population parameter, assuming that the requirements are satisfied. a. Mean b. Proportion c. Standard deviation 9.True or False Determine whether the given statements are true or false. a. In hypothesis testing, it is never valid to form a conclusion of supporting the null hypothesis. b. The conclusion of “fail to reject the null hypothesis” has exactly the same meaning as “accept the null hypothesis.” c. If correct methods of hypothesis testing are used with a large simple random sample that satisfies the test requirements, the conclusion will always be true. d. When conducting a hypothesis test about the claimed proportion of adults who have current driving licenses, the problems with a convenience sample can be overcome by using a larger sample size. e. When repeating the same hypothesis test with different random samples of the same size, the conclusions will all be the same. 10. Robust Explain what is meant by the statements that the t test for a claim about m is robust, but the x2 test for a claim about s is not robust. 1.Job Search A Gallup poll of 195,600 employees showed that 51% of them were actively searching for new jobs. Use a 0.01 significance level to test the claim that the majority of employees are searching for new jobs. 2.Tour de France Listed below are the mean speeds (km/h) of recent winners of the Tour de France bicycle race. Use these speeds with a 0.05 significance level to test the claim that these recent mean winning speeds are not significantly different from the 27.2 km>h mean winning speed from the first few Tour de France races in the early 20th century. 40.3 39.6 40.0 39.9 40.9 40.6 41.7 40.8 39.0 40.5 40.3 39.6 39.8 39.9 40.5 40.7 39.6 39.6 41.0 40.2 3. Red Blood Cell Count A simple random sample of 40 adult males is obtained, and the red blood cell count (in cells per microliter) is measured for each of them, with these results: n = 40, x = 4.932 million cells per microliter, s = 0.504 million cells per microliter (from Data Set 1 “Body Data” in Appendix B). Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 5.4 million cells per microliter, which is often used as the upper limit of the range of normal values. Does the result suggest that each of the 40 males has a red blood cell count below 5.4 million cells per microliter? 4.Perception and Reality In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won (based on data from ICR Survey Research Group). Use a 0.05 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions? 5.Type I Error and Type II Error a. In general, what is a type I error? In general, what is a type II error? b. For the hypothesis test in Exercise 4 “Perception and Reality,” write a statement that would be a type I error, and write another statement that would be a type II error. Review Exercises
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