Q18Single correct3 Marks1 Sep 2024

Consider $36$ samples $X_1, X_2, \ldots, X_{36} \sim \text{iid Normal}(\mu, 36)$. Let the null and alternate hypothesis be $H_0: \mu = 150$ and $H_A: \mu \neq 150$. Suppose $T = \frac{X_1 + X_2 + \ldots + X_{36}}{36}$. Consider a test that rejects $H_0$ if $|T - 150| > c$ for some constant $c$. What should be the critical value for the test at a significance level of $0.05$?

A

$F_Z^{-1}(0.025)$

B

$-F_Z^{-1}(0.025)$

C

$150 + F_Z^{-1}(0.025)$

D

$150 - F_Z^{-1}(0.025)$