Appraisal of 98.6 Degrees F, the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold August Wundrlich") 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. (5 points) Test the hypotheses \( H_{0}: \mu=98.6 \) versus \( H_{0}: \mu \neq 98.6 \), using \( \alpha=0.05 \).
b. (2 points) Compute the power of the test if the true mean female body temperature is as low as 98.0 . Use the OC Curves.
c. (2 points) 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 ? Use the OC Curves.
d. (2 points) Explain how the question in part (a) could be answered by constructing a two-sided confidence interval on the mean female body temperature.