Question

A population consists of the following five values: 6, 6, 14, 18, and 23. a. Not available in Connect. b. By listing all samples of size 3, compute the mean of the distribution of the sample mean and the population mean. Compare the two values. (Round the final answers to 2 decimal places.) Sample means Population mean Both means are c. Compare the dispersion in the population with that of the sample means. Hint: Use the range as measure of dispersion. The dispersion of the population is than that of the sample means.

Answer 1

Population consists of 5 values.

So, number of samples of size 3 that can be made out of it are ₅C₃ = 5!/(2!*(5-2)! = 5!/(2!*3!) = 10

List of all samples of size 3 made out of population

Sample	Values	Sum	Mean
1	6,6,14	26	8.67
2	6,6,18	30	10.00
3	6,6,23	35	11.67
4	6,14,18	38	12.67
5	6,14,23	43	14.33
6	6,18,23	47	15.67
7	6,14,18	38	12.67
8	6,14,23	43	14.33
9	6,18,23	47	15.67
10	14,18,23	55	18.33
		Sum of Sample Means =	134.00

Comparison between mean of the sample means and population mean

Mean of the distribution of the sample mean = Sum of Sample Means/No. of samples of size 3 that can be made

Mean of the distribution of the sample mean = 134/10 = 13.40

Population Mean = (6+6+4+18+23)/5 = 57/5 = 11.40

The mean of the sample means (13.4) is greater than the population mean (11.4).

Compare the dispersion in the population with that of the sample mean

Range of the population is 23-6 = 17
Range of the sample means is 18.33-8.67 = 9.66

Thus, it can be inferred that the sample means are less dispersed than the population.