Arandom 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. (i suggest doing this problem with a calculator and table as practice for exams. you may check your answers with r if you wish.)

(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.