Question

A population with a size of 4 has a mean of 5.41 and a variance of 6.8. The sampling distribution has a sample size of 3 and all possible samples are drawn without replacements. Find the mean, variance, and standard deviation.

Answer 1

(a). The mean of sampling distribution is:

\mu \:_{\overline{x}}=\frac{sum\:of\:all\:samples}{number\:of\:samples}=\frac{6}{3}=2

(b). The variance of sampling distribution is:

The variance $\sigma ^2_{\overline{x}}$ of the sampling distribution means is obtained by subtracting the mean 2 from each number, squaring the result, adding all 3 numbers obtained, and dividing by 3. The final result is:

$\sigma ^2_{\overline{x}}=\frac{2}{3}=0.6667$

(c). The standard deviation of sampling distribution is:

Standard deviation is the square root of variance obtained in b

$\sigma _{\overline{x}}=\sqrt{\sigma ^2_{\overline{x}}}$

\sigma \:_{\overline{x}}=\sqrt{0.6667}=0.8165