A population consists of the following five values: 9, 9, 15, 22, and 28.

Question

A population consists of the following five values: 9, 9, 15, 22, and 28.

 

a. Not available

 

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	(Click to select)  equal  not equal

 

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  (Click to select)  greater  smaller  than that of the sample means.

Answer 1

What does part a) wants you to do?

For part b). I don't know of any "short-cut" to do this problem. To calculate the sample mean: I think you will need to literally list all the possible subsets of size=3. Then go back & calculate the mean for each subset. Then, go back and calculate the mean of all those means (mean of each subset). This is often called the 'standard error of the mean', and tells you how well you are estimating the mean of the population of interest.

To calculate the population mean, simply find the mean of the 5 values given as the 'population'.

For part c) just follow the directions given, and use the range (highest & lowest) to estimate the dispersion in the population and the list of sample means for each subset.

FYI: I expect the population dispersion to be greater than that of the sample means, it usually is.