464 CHAPTER 9 Inferences from Two Samples Statistical Literacy and Critical Thinking 1.Independent Samples Which of the following involve independent samples? a. Data Set 4 “Measured and Reported” includes measured heights matched with the heights that were reported when the subjects were asked for those values. b. Data Set 6 “Births” includes birth weights of a sample of baby boys and a sample of baby girls. c. Data Set 1 “Body Data” includes a sample of pulse rates of 147 women and a sample of pulse rates of 153 men. 2.Pulse Rates of Women and Men Using the samples of women and men included in Data Set 1 “Body Data,” we get this 95% confidence interval estimate of the difference between the population mean of pulse rates (bpm) of women and the population mean of pulse rates (bpm) of men: 1.7bpm 6 m1 - m2 6 7.2bpm. In this confidence interval, women correspond to population 1 and men correspond to population 2. a. What does the confidence interval suggest about equality of the mean pulse rate of women and the mean pulse rate of men? b. Write a brief statement that interprets the confidence interval. c. Express the confidence interval with measures from men being population 1 and measures from women being population 2. 3.Hypothesis Tests and Confidence Intervals for Pulse Rates a. Exercise 2 includes a confidence interval. If you use the P-value method or the critical value method from Part 1 of this section to test the claim that women and men have the same mean pulse rates, will the hypothesis tests and the confidence interval result in the same conclusion? b. In general, if you conduct a hypothesis test using the methods of Part 1 of this section, will the P-value method, the critical value method, and the confidence interval method result in the same conclusion? c. Assume that you want to use a 0.01 significance level to test the claim that the mean pulse rate of women is greater than the mean pulse rate of men. What confidence level should be used if you want to test that claim using a confidence interval? 4. Degrees of Freedom For Example 1 on page 457, we used df = smaller of n1 - 1 and n2 - 1, we got df = 11, and the corresponding critical value is t = -1.796 (found from Table A-4). If we calculate df using Formula 9-1, we get df = 19.370, and the corresponding critical value is t = -1.727. How is using the critical value of t = -1.796 “more conservative” than using the critical value of t = -1.727? In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1−1 and n2−1.) 5.Better Tips by Giving Candy An experiment was conducted to determine whether giving candy to dining parties resulted in greater tips. The mean tip percentages and standard deviations are given below along with the sample sizes (based on data from “Sweetening the Till: The Use of Candy to Increase Restaurant Tipping,” by Strohmetz et al., Journal of Applied Social Psychology, Vol. 32, No. 2). a. Use a 0.05 significance level to test the claim that giving candy does result in greater tips. 9-2 Basic Skills and Concepts
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