Question

Sampling with replacement

1. A researcher is interested in drawing a sample of potential voters from a population of 10 individuals. She settles on a sample size of 5, and sends out random invitations to 5 of the voters, by picking their names randomly from a list. How many possible samples could she draw from this population?

Sampling without replacement

2. The researcher realizes that she made a mistake! She accidentally asked the selected some of the same voters more than once. She updates her sampling method to only sample each individual once. She again samples 5 voters. How many possible samples could she draw from this population?
3. Let’s say we have the following data from a population:

7

10

15

a) What is the mean of this population?

b) If we were to sample with replacement, for a sample size of 2, how many samples could we get?

4. Write out all the possible samples we could get, and calculate the mean for each of them. This is called the sampling distribution of the mean.

Sample	Sample Mean (M)

5. What is the mean of the Sample Means? (the mean of the sampling distribution)

μ_M= _____

6. Using the following formula, calculate the variance of the sampling distribution from #4 (use the same sample and sample means here to fill in the table). This formula indicates how much each score deviates from the mean of the sampling distribution.

σ²_M= (M-μ_M)² / Nⁿ

Sample	Sample Mean (M)	(M-μM)2	(M-μM)2/ N2

Answer 1

Sample	Sample Mean
7,7	7
7,10	8.5
7,15	11
10,7	8.5
10,10	10
10,15	12.5
15,7	11
15,10	12.5
15,15	15

Mean of the sampling mean is = = 96/9 = 10.67