Question

A population consists of five (5) measurements 2, 3, 6, 5, and 7. 

1. What is the mean of the population?
2. What is the variance of the population?
3. How many different samples of size 𝑛 = 2 can be drawn from the population?
4. What is the mean of the sampling distribution of the sample means?
5. What is the variance of the sampling distribution of the sample means with a sample size of 2?

Answer 1

1. Mean $= \frac{2+3+6+5+7}{5}=4.6$

2. Variance $= \frac{1}{5-1}( (2-4.6)^2 + (3-4.6)^2 + (6-4.6)^2+ (5-4.6)^2+(7-4.6)^2 )$

$= \frac{1}{4}(6.76+2.56+1.96+0.16+5.76) \\ = 4.3$

3. Number of sample $= \frac{5!}{2!(5-2)!} = \frac{20}{20}=10$

4.

The mean of the sampling distribution of the sample means = 4.6

5. The variance of the sampling distribution of the sample means = 1.43