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 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 interior temperature.