Question

A population consists of the following five values: 2, 2, 30, 9, 30.

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 answer to the nearest whole number.)

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.

A population consists of the following five values: 2, 2, 30, 9, 30.

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 answer to the nearest whole number.)

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

Solution:

b. Mean of the distribution of the sample Mean =  Population Mean

c.The dispersion of the population is greater than or equal to that of the sample means

Explanation:

We have a total of 5 observations in the population space and they are 2,2,30,9,30

The population mean = Sum of total observations/Number of observations

= (2+2+30+9+30)/5 = 73/5 = 14.6

Now as we have 5 observations, we have to choose 3 observations randomly. This can be done in 5C3 = 10 ways.

All the possible 5 sample spaces are listed in the table below and sample means are calculated accordingly:

Samples	Sample Space			Sample mean	Population Mean	Dispersion of the sample = Range (Larger value - Smaller value)
Sample 1	2	2	30	11.33	14.60	28
Sample 2	2	2	9	4.33	14.60	7
Sample 3	2	2	30	11.33	14.60	28
Sample 4	2	30	9	13.67	14.60	28
Sample 5	2	30	30	20.67	14.60	28
Sample 6	2	9	30	13.67	14.60	28
Sample 7	30	9	30	23.00	14.60	21
Sample 8	2	30	9	13.67	14.60	28
Sample 9	2	30	30	20.67	14.60	28
Sample 10	2	9	30	13.67	14.60	28
Mean of Sample Mean				14.60		Dispersion of population = 28

We observed that mean of all the sample means = 14.60

Also Population Mean = 14.60

Hence Mean of all sample means = Population mean

As observed in the table we have a sample Dispersion = Larger value - Smaller value

Hence dispersion of population = 30-2 = 28