Solve the following

Question

Random samples with size 4 are drawn from the population containing the values 19, 14, 26, 31, 53 and 44

a. Construct a sampling distribution of the sample means.

b. Find the mean of the sample means.

c. Compute the standard error of the sample means.

Answer 1

To construct the sampling distribution, form all possible samples of size 4 for the given list of numbers (6 choose 4). There should be 15. I would use Google Sheets, Excel, or the TI-84 to help you generate the combinations.

Then, calculate the individual sample means, then take the mean of the sample means. You should get 31.17 from this.

Then, calculate the standard error of the sample means by using the standard deviation (population) formula. You should get 4.30 from this.

Hope this was helpful.