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 9.2.5 Output from a software package follows: One-Sample Z: Test of mu = 99 vs > 99 The assumed standard deviation = 2.5 Variable N Mean StDev SE Mean Z P x 12 100.039 2.365 ? 1.44 0.075 a) Fill in the missing items. What conclusions would you draw? b) Is this a one-sided or a two-sided test? c) If the hypothesis had been H0: = 98 versus H0: > 98, would you reject the null hypothesis at the 0.05 level of significance? Can you answer this without referring to the normal table? d) Use the normal table and the preceding data to construct a 95% lower bound on the mean. e)What would the P-value be if the alternative hypothesis is H1: 99?

9.2.8 Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their speed. It occurs above approximately 50 meters per second when pressure drops sufficiently to allow the water to dissociate into water vapor, forming a gas bubble behind the vehicle. When the gas bubble completely encloses the vehicle, supercavitation is said to occur. Eight tests were conducted on a scale model of an undersea vehicle in a towing basin with the average observed speed x=102.2 meters per secondx=102.2 meters per second. Assume that speed is normally distributed with known standard deviation = 4 meters per second. a) Test the hypothesis H0: = 100 versus H1: < 100 using = 0.05. b) What is the P-value for the test in part (a)?

9.3.1 A hypothesis will be used to test that a population mean equals 10 against the alternative that the population mean is greater than 10 with unknown variance. What is the critical value for the test statistic T0 for the following significance levels? a) = 0.01 and n = 20 1. b) = 0.05 and n = 12 1. c) = 0.10 and n = 15

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.

9.3.7 An article in Growth: A Journal Devoted to Problems of Normal and Abnormal Growth ["Comparison of Measured and Estimated Fat-Free Weight, Fat, Potassium and Nitrogen of Growing Guinea Pigs" (1982, Vol. 46(4), pp. 306-321)] reported the results of a study that measured the body weight (in grams) for guinea pigs at birth. 421.0 452.6 456.1 494.6 373.8 90.5 110.7 96.4 81.7 102.4 241.0 296.0 317.0 290.9 256.5 447.8 687.6 705.7 879.0 88.8 296.0 273.0 268.0 227.5 279.3 258.5 296.0 a. Test the hypothesis that mean body weight is 300 grams. Use = 0.05. b. What is the smallest level of significance at which you would be willing to reject the null hypothesis? c. Explain how you could answer the question in part (a) with a two-sided confidence interval on mean body weight.

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.

9.3.11 Exercise 6.2.8 gave data on the heights of female engineering students at ASU. a) Can you support a claim that the mean height of female engineering students at ASU is at least 65 inches? Use = 0.05. Find the P-value. DATA FOR THE PROBLEM The female students in an undergraduate engineering core course at ASU self-reported their heights to the nearest inch. The data follow. Construct a stem-and-leaf diagram for the height data and comment on any important features that you notice. Calculate the sample mean, the sample standard deviation, and the sample median of height. 62 64 61 67 65 68 61 65 60 65 64 63 59 68 64 66 68 69 65 67 62 66 68 67 66 65 69 65 69 65 67 67 65 63 64 67 65 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.