Q26Single correct3 Marks24 Dec 2023

Consider 100 samples $X_1, X_2, \dots, X_{100} \sim \text{iid Normal}(\mu, 25)$. Let the null and alternative hypothesis be $H_0: \mu = -2$ and $H_A: \mu = 2$. Suppose $T = \frac{X_1 + X_2 + \dots + X_{100}}{100}$. Consider a test that rejects $H_0$ if $T > c$ for some constant $c$. What is the significance level of the test in terms of '$c$'?

A

$F_Z(2(c+2))$

B

$1 - F_Z(2(c+2))$

C

$F_Z(2(c-2))$

D

$1 - F_Z(2(c-2))$