446 CHAPTER 8 Hypothesis Testing with Two Samples Extending Concepts 21. In Exercise 15, use technology to perform the hypothesis test with a P@value. Compare your result with the result obtained using rejection regions. Are they the same? 22. In Exercise 18, use technology to perform the hypothesis test with a P@value. Compare your result with the result obtained using rejection regions. Are they the same? Constructing Confidence Intervals for Md To construct a confidence interval for md, use the inequality below. d - tc sd1 n 6 md 6 d + tc sd1 n In Exercises 23 and 24, construct the indicated confidence interval for md. Assume the populations are normally distributed. 23. Drug Testing A sleep disorder specialist wants to test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the night. To do so, the specialist randomly selects 16 patients and records the number of hours of sleep each gets with and without the new drug. The table shows the results of the two-night study. Construct a 90% confidence interval for md. Patient 1 2 3 4 5 6 7 8 Hours of sleep (without the drug) 1.8 2.0 3.4 3.5 3.7 3.8 3.9 3.9 Hours of sleep (using the drug) 3.0 3.6 4.0 4.4 4.5 5.2 5.5 5.7 Patient 9 10111213141516 Hours of sleep (without the drug) 4.0 4.9 5.1 5.2 5.0 4.5 4.2 4.7 Hours of sleep (using the drug) 6.2 6.3 6.6 7.8 7.2 6.5 5.6 5.9 24. Herbal Medicine Testing A sleep disorder specialist wants to test whether herbal medicine increases the number of hours of sleep patients get during the night. To do so, the specialist randomly selects 14 patients and records the number of hours of sleep each gets with and without the medicine. The table shows the results of the two-night study. Construct a 95% confidence interval for md. Patient 1 2 3 4 5 6 7 Hours of sleep (without medicine) 1.0 1.4 3.4 3.7 5.1 5.1 5.2 Hours of sleep (using medicine) 2.9 3.3 3.5 4.4 5.0 5.0 5.2 Patient 8 9 1011121314 Hours of sleep (without medicine) 5.3 5.5 5.8 4.2 4.8 2.9 4.5 Hours of sleep (using medicine) 5.3 6.0 6.5 4.4 4.7 3.1 4.7
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