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.

(a) Test the hypothesis H0:  98.6 versus , using   0.05. Find the P-value.

(b) Check the assumption that female body temperature is normally distributed.

(c) Compute the power of the test if the true mean female body temperature is as low as 98.0.

(d) What sample size would be required to detect a true mean female body temperature as low as 98.2 if we 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 two-sided confidence interval on the mean female body temperature.