Answer to Question #254492 in Statistics and Probability for hedi

Question

Given the population 1, 3, 4, 6 and 8. Suppose samples of size 3 are drawn from this population. What is the mean and standard deviation of the Sampling Distribution?

Answer 1

Population size (N) = 5

Sample size (n) = 3

Total number of possible samples is:

$\dbinom{N}{n}=\dbinom{5}{3}=10$

Mean and Standard deviation of sampling distribution:

$E(\bar{X})=\sum\bar{X}f(\bar{X})=\frac{132}{30}=4.4$

So, the mean of the sampling distribution of the sample means is 4.4.

$Var(\bar{X})=\sum \bar{X}^{2}f(\bar{X})-(\sum\bar{X}f\bar{X})^{2}$

$Var(\bar{X})=\frac{1830}{90}-(\frac{132}{30})^{2}=\frac{73}{75}$

$\sqrt{Var(\bar{X})}=\sqrt{\frac{73}{75}}=0.9866$

So, standard deviation of the Sampling Distribution is 0.9866.