Consider set of observations Yi, i = 1, 2,... 40, which are supposed to be independent and identically normally distributed with mean µ and variance s^2.
Suggest the null hypothesis H0 : µ = 20 and two-sided alternative hypothesis H1 : µ ? 20. Give the t-test of this set of hypotheses based upon Y1,..., Y40 and a= 0.05. In the context of hypothesis test presented provide clear, explicit definitions of following terms.
(i) Type I error
(i) Type II error
(iii) Power of the test.