A quarterback threw 1 interception in his first game, 2 interceptions in his second game, and 5 inter-ceptions in his third game, and then he retired. Consider the values 1, 2, and 5 to be a population. Assume that samples of size 2 are randomly selected (with replacement) from the population. a. List the 9 different possible samples, and find the mean of each sample. b. What is the mean of the sample means from part (a)? c. Is the mean of the sampling distribution from part (b) equal to the mean of the population of the three listed values? Are those means always equal?
A quarterback threw 1 interception in his first game, 2 interceptions in his second game, and 5 inter-ceptions in his third game, and then he retired. Consider the values 1, 2, and 5 to be a population. Assume that samples of size 2 are randomly selected (with replacement) from the population.
a. List the 9 different possible samples, and find the
b. What is the mean of the sample means from part (a)?
c. Is the mean of the sampling distribution from part (b) equal to the mean of the population of the three listed values? Are those means always equal?
Given,
Population size (N) = 3, having elements 1,2 and 5.
Sample size (n) =2
The sample has to be drawn by simple random sampling with replacement (SRSWR).
Number of possible samples by SRSWR of size n from a population of size N = (N)^n
So the number of possible samples by SRSWR of size 2 from a population of size 3 will be (3)^2 = 9.
a.)
The List of all possible samples and their means are as follows:
| S.N. | Sample (a,b) | Mean()= |
| 1. | (1,1) | 1 |
| 2. | (1,2) | 1.5 |
| 3. | (1,5) | 3 |
| 4. | (2,1) | 1.5 |
| 5. | (2,2) | 2 |
| 6. | (2,5) | 3.5 |
| 7. | (5,1) | 3 |
| 8. | (5,2) | 3.5 |
| 9. | (5,5) | 5 |
| Total | 24 |
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