Q11Single correct3 Marks13 Apr 2025

Suppose $X \sim N(\mu, \sigma^2)$ with an unknown $\sigma$. For $n = 16$ i.i.d. samples of $X$, the observed sample mean is $10.2$ and the sample standard deviation is $3$. Let the null and alternative hypothesis be $H_0: \mu = 9.5$ and $H_A: \mu > 9.5$. Suppose $T = \frac{\bar{X} - 9.5}{3/\sqrt{16}}$. Consider a test that rejects $H_0$ if $T > c$ for some constant $c$. What is the level of significance in terms of 'c'?

A

$1 - F_{t_{15}}\left( \frac{4(c - 9.5)}{3} \right)$

B

$1 - F_{t_{16}}\left( \frac{4(c - 9.5)}{3} \right)$

C

$1 - F_{Z}\left( \frac{4(c - 9.5)}{3} \right)$

D

$F_{Z}\left( \frac{4(c - 9.5)}{3} \right)$