480 CHAPTER 9 Inferences from Two Samples 21. Height and Arm Span Supposedly, a person’s height is approximately equal to their arm span. Refer the Data Set 3 “ANSUR II 2012” and use the heights and arm spans (cm) of the 4082 males. Use a 0.05 significance level to test the claim that for males, their height is the same as their arm span. 22.Do Men Talk Less than Women? Repeat Exercise 6 “Do Men Talk Less than Women” using all of the data in the first two columns of Data Set 14 “Word Counts” in Appendix B. 23.Heights of Mothers and Daughters Repeat Exercise 13 “Heights of Mothers and Daughters” using all of the heights of mothers and daughters listed in Data Set 10 “Family Heights” in Appendix B. 24.Heights of Fathers and Sons Repeat Exercise 14 “Heights of Fathers and Sons” using all of the heights of fathers and sons listed in Data Set 10 “Family Heights” in Appendix B. 25.Heights of Fathers and Sons a. Repeat Exercise 14 using a confidence interval constructed with the methods of this section. b. Repeat Exercise 14 using a confidence interval constructed by using the bootstrap method described in Section 7-4. c. Compare the results from parts (a) and (b). 9-3 Beyond the Basics Key Concept In this section we present the F test for testing claims made about two population variances (or standard deviations). The F test (named for statistician Sir Ronald Fisher) uses the F distribution introduced in this section. The F test requires that both populations have normal distributions. Instead of being robust, this test is very sensitive to departures from normal distributions, so the normality requirement is quite strict. Part 1 describes the F test procedure for conducting a hypothesis test, and Part 2 gives a brief description of two alternative methods for comparing variation in two samples. 9-4 Two Variances or Standard Deviations PART 1 F Test with Two Variances or Standard Deviations The following Key Elements box includes elements of a hypothesis test of a claim about two population variances or two population standard deviations. The procedure is based on using the two sample variances, but the same procedure is used for claims made about two population standard deviations. The actual F test could be two-tailed, left-tailed, or right-tailed, but we can make computations much easier by stipulating that the larger of the two sample variances is denoted by s2 1. It follows that the smaller sample variance is denoted as s 2 2. This stipulation of denoting the larger sample variance by s2 1 allows us to avoid the somewhat messy problem of finding a critical value of F for the left tail.
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