A random sample of size n = 10 is taken from a large population. Let µ be the unknown population mean. A test is planned of H0 : µ = 12 vs. HA : µ 6= 12 using α = 0.1. A QQ plot indicates it it is reasonable to assume a normal population. From the sample, ¯x = 14.2 and s = 4.88.

a. Since the data leave it plausible that the population is normal, and the population standard deviation σ is unknown, a t-test is appropriate. Compute the p-value of the test. Do you reject or not reject H0?
b. Compute the power of the test if the true population mean is µA = 15.
c. Using s = 4.88 as our best guess of σ, approximately what sample size would be required to achieve a power of 0.8 if the true population mean is µA = 15? Give your answer as the smallest whole number that meets the criterion.