Consider i.i.d. observations $X_{1}, \ldots, X_{n} \sim N\left(\mu, \sigma^{2} ight) $ with both $\mu, \sigma^{2}$ unknown. (a) Construct an $\alpha$-level test for $H_{0}: \mu=0$ vs $H_{1}: \mu eq 0$ using $t$ distribution. (b) Construct an $\alpha$-level test for $H_{0}: \sigma^{2} \leq 1$ vs $H_{1}: \sigma^{2} \geq 1$ using chi-squared distribution. SP.PB. 113