9-3 Matched Pairs 469 22. Are We Getting Taller? Example 1 used heights of small samples of males from Data Set 2 “ANSUR I 1988” and from Data Set 3 “ANSUR II 2012.” Repeat Example 1 using the 1774 heights of males from the ANSUR I 1988 data set and the 4082 heights of males from the ANSUR II 2012 data set. Do the larger samples provide sufficient evidence to suggest that people are getting taller? 23.Do Men Talk Less Than Women? Refer to Data Set 14 “Word Counts” and use the measured word counts from men in the third column (“M2”) and the measured word counts from women in the fourth column (“F2”). Use a 0.05 significance level to test the claim that men talk less than women. 24. Queues Repeat Exercise 18 using all of the waiting times from the two line configuration and the single line configuration in Data Set 30 “Queues” in Appendix B. 25. Pooling Repeat Exercise 14 “IQ and Lead Exposure” by assuming that the two population standard deviations are equal, so s1 = s2. Use the appropriate method from Part 2 of this section. Does pooling the standard deviations yield results showing greater significance? 26.Degrees of Freedom In Exercise 20 “Blanking Out on Tests,” using the “smaller of n1 - 1 and n2 - 1” for the number of degrees of freedom results in df = 15. Find the number of degrees of freedom using Formula 9-1. In general, how are hypothesis tests and confidence intervals affected by using Formula 9-1 instead of the “smaller of n1 - 1 and n2 - 1”? 27. No Variation in a Sample An experiment was conducted to test the effects of alcohol. Researchers measured the breath alcohol levels for a treatment group of people who drank ethanol and another group given a placebo. The results are given below (based on data from “Effects of Alcohol Intoxication on Risk Taking, Strategy, and Error Rate in Visuomotor Performance,” by Streufert et al., Journal of Applied Psychology, Vol. 77, No. 4). Use a 0.05 significance level to test the claim that the two sample groups come from populations with the same mean. Treatment Group: n1 = 22, x1 = 0.049, s1 = 0.015 Placebo Group: n2 = 22, x2 = 0.000, s2 = 0.000 9-2 Beyond the Basics Key Concept This section presents methods for testing hypotheses and constructing confidence intervals involving the mean of the differences of the values from two populations that consist of matched pairs. The pairs must be matched according to some relationship, such as these: ■ Before>after measurements from the same subjects ■ IQ scores of husbands and wives ■ Measured and reported weights from a sample of subjects Good Experimental Design Many experiments have been conducted to test the effectiveness of drug treatments in lowering blood pressure. When designing such experiments to test the effectiveness of a treatment, there are different approaches that could be taken, such as these: 1. Measure the blood pressure of each subject before and after the treatment, then analyze the “before – after” differences. 9-3 Matched Pairs continued
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