Question

Let $X_1, X_2, \ldots, X_{10}$ be a random sample from the $N(3,4)$ distribution, and let $Y_1, Y_2, \ldots, Y_{15}$ be a random sample from the $N(-3,6)$ distribution. Assume that the two samples are drawn independently. Define:
$\bar{X} = \frac{1}{10} \sum_{i=1}^{10} X_i$
$\bar{Y} = \frac{1}{15} \sum_{j=1}^{15} Y_j$
$S = \sqrt{\frac{1}{9} \sum_{i=1}^{10} (X_i - \bar{X})^2}$
Then the distribution of $U = \frac{\sqrt{5}(\bar{X} + \bar{Y})}{S}$ is:

• A. $N\left(0, \frac{4}{5}\right)$
• B. $\chi^2_9$
• C. $t_9$
• D. $t_{23}$

Answer 1

Answer: (C)

$t_9$

Answer 2

The correct option is (C): $t_9$