Question

Consider all samples of size 5 from this population: 2 5 6 8 10 12 13

a) Compute the mean (μ) and standard deviation (σ) of the population.

b) Calculate the mean and the standard deviation of the sampling distribution of the sample means.

Answer 1

$a:\\\mu =\frac{2+5+6+8+10+12+13}{7}=8\\\sigma =\sqrt{\frac{\left( 2-8 \right) ^2+\left( 5-8 \right) ^2+\left( 6-8 \right) ^2+\left( 8-8 \right) ^2+\left( 10-8 \right) ^2+\left( 12-8 \right) ^2+\left( 13-8 \right) ^2}{7}}=3.6645\\b:\\\mu _{\bar{x}}=\mu =8.5\\\sigma _{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{3.6645}{\sqrt{5}}=1.63881$