18.26 Generating a sampling distribution. Let us illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The population is the scores of 10 students on an exam:
| Student: | 0 | 1 | 2 | 3 | 4 |
| Score: | 82 | 62 | 80 | 58 | 72 |
| Student: | 5 | 6 | 7 | 8 | 9 |
| Score: | 73 | 65 | 66 | 74 | 62 |
The parameter of interest is the mean score in this population. The sample is an SRS of size drawn from the population. Because the students are labeled 0 to 9, a single random digit from Table A chooses one student for the sample.
(a) Find the mean of the 10 scores in the population. This is the population mean.
(b) Use Table A to draw an SRS of size 4 from this population. Write the four scores in your sample and calculate the mean of the sample scores. This statistic is an estimate of the population mean.
(c) Repeat this process 10 times using different parts of Table A. Make a histogram of the 10 values of . You are constructing the sampling distribution of . Is the center of your histogram close to the population mean you found in part (a)?