Question: It is given that X - N(µ,16). It is desired to test the null hypothesis µ = 12 against the alternative hypothesis µ > 12, with the probability of a Type I error being 1%. A random sample of 15 observations (sample size) of X is taken and the sample mean X^¯ is taken to be the test statistic.

(i) Find the acceptance and rejection regions.

(ii) For the case µ = 15, find the probability of a Type II error.

(iii) Derive and state the power function for µ > 12.

(iv) Compute the minimum sample sizes for power(15) > 0.9 and power(15) > 0.99.