題組內容

2. (15%) Consider a random sample of size 20 from a normal distribution, $X_i \sim N(\mu, \sigma^2)$, and suppose that $\bar{x} = 11$ and $s^2 = 16$.



(a) Assume it is known that $\sigma^2 = 4$, test $H0: \mu \ge 12$ versus $Ha: \mu < 12$ at the significance level $\alpha = 0.01$.