9.1.1 State whether each of the following situations is a correctly stated hypothesis testing problem and why. a) H0: = 25, H1: 25 a. b) H0: > 10, H1: = 10 a. c) H0:x=50H0:x=50, H1:x50H1:x50 a. d) H0: p = 0.1, H1: p = 0.5 a. e) H0: s = 30, H1: s > 30 a.

9.2.2 A hypothesis will be used to test that a population mean equals 5 against the alternative that the population mean is less than 5 with known variance . What is the critical value for the test statistic Z0 for the following significance levels? a) 0.01 b) 0.05 c) 0.10

9.3.6 An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp. 59-75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59. a) Test the hypotheses H0: = 22.5 versus H1: 22.5, using = 0.05. Find the P-value. b) Check the assumption that interior temperature is normally distributed. c) Compute the power of the test if the true mean interior temperature is as high as 22.75. d) What sample size would be required to detect a true mean interior temperature as high as 22.75 if you wanted the power of the test to be at least 0.9? e) Explain how the question in part (a) could be answered by constructing a twosided confidence interval on the mean interior temperature.

9.3.9 A 1992 article in the Journal of the American Medical Association ("A Critical Appraisal of 98.6 Degrees F, the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wunderlich") reported body temperature, gender, and heart rate for a number of subjects. The body temperatures for 25 female subjects follow: 97.8, 97.2, 97.4, 97.6, 97.8, 97.9, 98.0, 98.0, 98.0, 98.1, 98.2, 98.3, 98.3, 98.4, 98.4, 98.4, 98.5, 98.6, 98.6, 98.7, 98.8, 98.8, 98.9, 98.9, and 99.0. Test the hypothesis H0: = 98.6 versus H1: 98.6, using = 0.05. Find the P-value.

9.5.3 An article in the British Medical Journal ["Comparison of Treatment of Renal Calculi by Operative Surgery, Percutaneous Nephrolithotomy, and Extra-Corporeal Shock Wave Lithotripsy" (1986, Vol. 292, pp. 879-882)] repeated that percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 of 350 patients. The traditional method was 78% effective. a) Is there evidence that the success rate for PN is greater than the historical success rate? Find the P-value.

9.5.6 A computer manufacturer ships laptop computers with the batteries fully charged so that customers can begin to use their purchases right out of the box. In its last model, 85% of customers received fully charged batteries. To simulate arrivals, the company shipped 100 new model laptops to various company sites around the country. Of the 100 laptops shipped, 96 of them arrived reading 100% charged. Do the data provide evidence that this model's rate is at least as high as the previous model? Test the hypothesis at = 0.05.