Question

Record the weight (in kilogram) of five (5) members in your household. Draw random samples of size  n = 2 from these weights. 

1. List all possible samples and compute the mean of each sample. 

2. Construct the sampling distribution of the sample means. 

3. Find mean (μ) and the standard deviation (σ) of the population. 

4. Find the mean, variance and standard deviation of the sampling distribution of the sample means.

Answer 1

52, 63, 74, 69, 82

$Number = \frac{N!}{n!(N-n)!} \\ n = 2 \\ Number = \frac{5!}{2!(5-2)!} = 10$

1.

2. The sampling distribution of the sample means

3. $\mu = \frac{52+ 63+ 74+ 69+ 82}{5} = 68$

$\sigma = \sqrt{ \frac{1}{5-1}((52-68)^2 +...+(82-68)^2)} = 11.33$

4.

$mean = \frac{57.5+...+78}{10} = 68 \\ variance = \frac{1}{10-1}( (57.5-68)^2+...+(78-68)^2 ) = 42.833 \\ standard \; deviation = \sqrt{42.833} = 6.544$