Question

A population consists of the numbers 5, 7, 9,

11, 12, and 15. List all possible sample size of

2 from this population and give the following:

•A. Determine the number of sets of all possible random samples that

can be drawn from the given population.

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

• C. Construct the sampling distribution.

•D. Construct a histogram of the sampling distribution of the means.

Answer 1

A) The number of possible samples is $C(6,2)=15$

B) All possible samples and the means

C) Sampling Distribution

$P(X=6)=P(X=7)=P(X=8.5)=P(X=9)=P(X=9.5)=P(X=11)=P(X=10.5)=P(X=12)=P(X=11.5)=P(X=13)=P(X=13.5)=\frac{1}{15}$

$P(X=8)=P(X=10)=\frac{2}{15}$

D) Histogram