Question: Suppose a sample of n = 25 items is drawn from a population described by a Normal distribution with standard deviation σ = 15, and that the sample mean of the 25 values is 96.4. Derive a 95% confidence interval for µ, the (unknown) mean of this distribution, and use your confidence interval to test, at the 5% significance level, the hypothesis H0 : µ = 100 against the general (two-sided) alternative H1 : µ = 100.