Question

Dan works in an insurance company. Last January, he was able to insure 2 persons. Last February, he was able to insure 3 persons. Last March, he was able to insure 5 persons. Assume that samples of size 2 are randomly selected with replacement from this population of three values. a. List down the 9 different possible samples. b. Find the mean of each sample. c. Find the mean of the sampling distribution of means. d. Identify the probability of each sample. e. Find the population mean. f. Compare the population mean with the mean of the sampling distribution of means.

Answer 1

a. Possible samples

$2,2$

$2,3$

$2,5$

$3,2$

$3,3$

$3,5$

$5,2$

$5,3$

$5,5$

b. Sample means

c. Mean of sampling distribution of means$=\frac{2+2.5+3.5+2.5+3+4+3.5+4+5}{9}=\frac{30}{9}=3.33$

d. Probability of each sample is $\frac{1}{9}$

e. Population mean $=\frac{2+3+5}{3}=\frac{10}{3}=3.33$

f. The population mean is equal to the mean of the sampling distribution of means