Question: 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 5 6 7 8 9
Score: 82 62 80 58 72 73 65 66 74 62
The parameter of interest is the mean score in this population. The sample is an SRS of size n = 4 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 x¯ 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 x¯. You are constructing the sampling distribution of x¯. Is the center of your histogram close to the population mean you found in (a)?