Question

A population consists of the following five values: 2, 2, 3, 5, and 7.

1. List all samples of size 3, and compute the mean of each sample.

2. Compute the mean of the distribution of sample means and the population mean. Compare the two values.

Answer 1

a)without replacement:

below is sampling distribution of mean of each sample:

		sample
(x1,x2)		mean(xbar)
(2,2,3)		2.33
(2,2,5)		3.00
(2,2,7)		3.67
(2,3,5)		3.33
(2,3,7)		4.00
(2,5,7)		4.67
(2,3,5)		3.33
(2,3,7)		4.00
(2,5,7)		4.67
(3,5,7)		5.00

b)

mean of the distribution of sample mean=(2.33+3+3.67+3.33+4+4.67+3.33+4+4.67+5)/10=3.80

population mean =(2+2+3+5+7)/5=3.80

both mean of the distribution of sample means and the population mean are equal