9-3 Matched Pairs 473 t 5 0 a5 0.05 Test Statistic: t 5 0.778 Critical Value: t 5 1.895 (b) Critical Value Method FIGURE 9-3 Hypothesis Test with Matched Pairs t 5 0 P-value: 0.231 Test Statistic: t 5 0.778 (a) P-Value Method YOUR TURN. Do Part (a) of Exercise 5 “Measured and Reported Weights.” INTERPRETATION We conclude that there is not sufficient evidence to support md 7 0 lb. There is not sufficient evidence to support the claim that for males, the measured weights tend to be higher than the reported weights. Based on the very small sample, it appears that males do not tend to report weights that are much lower than their actual weights. It is possible that a much larger sample would lead to a different conclusion. Confidence Interval for Estimating the Mean of the Differences Between Measured Weights and Reported Weights of Males EXAMPLE 2 Using the same sample data in Table 9-2, construct a 90% confidence interval estimate of md, which is the mean of the differences between measured weights and reported weights of males. By using a confidence level of 90%, we get a result that could be used for the hypothesis test in Example 1. (Because the hypothesis test is one-tailed with a significance level of a = 0.05, the confidence level should be 90%. See Table 8-1 on page 376.) SOLUTION REQUIREMENT CHECK The solution for Example 1 includes verification that the requirements are satisfied. Some technologies such as Statdisk, Minitab, XLSTAT, and the TI-83>84 Plus calculator will provide the confidence interval when asked politely. To manually find the confidence interval, use these sample statistics found in Example 1: n = 8, d = 1.425 lb, sd = 5.181216 lb and use the critical value of t = 1.895 (also found in Example 1). We first calculate the value of the margin of error E. E = ta>2 sd2 n = 1.895# 5.181216 2 8 = 3.4713301 We now find the confidence interval. d - E 6 md 6 d + E 1.425 - 3.4713301 6 md 6 1.425 + 3.4713301 -2.05 lb 6 md 6 4.90 lb Gender Gap in Drug Testing A study of the relationship between heart attacks and doses of aspirin involved 22,000 male physicians. This study, like many others, excluded women. The General Accounting Office criticized the National Institutes of Health for not including both genders in many studies because results of medical tests on males do not necessarily apply to females. For example, women’s hearts are different from men’s in many important ways. When forming conclusions based on sample results, we should be wary of an inference that extends to a population larger than the one from which the sample was drawn. continued
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