Question

Question 2 of 20: Select the best answer for the question. Population 1 Population2 44,12 4210 2. Independent random samples of 64 observations each are chosen from two normal populations with the means and standard deviations shown. Assume sample means. What is the standard deviation of the sampling distribution x? that x1 and x2 denote the two A. .375 B. .425 C..565 D..5

Answer 1

Given that,

For population 1:

Mean $(\mu_1)$ = 12 and standard deviation $(\sigma_1)$ = 4

sample size ( n ) = 64

We want to find, the standard deviation of the sampling distribution of $\bar x_1$

$\sigma_{\bar x_1} = \frac {\sigma_1}{\sqrt n } = \frac { 4}{\sqrt {64}} = \frac { 4}{8} = 0.5$

Answer: D) 0.5

Note: mean and standard deviation of the sampling distribution of sample mean are,

$\mu_{\bar x} = \mu$

$\sigma_{\bar x} = \frac {\sigma}{\sqrt n }$