Generating a sampling distribution. Let’s illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The population is the sizes of 10 medium-sized businesses where size is measured in terms of the number of employees. For convenience, the 10 companies have been labeled with the integers 0 to 9.

Company: 0 1 2 3 4 5 6 7 8 9 Size: 82 62 80 58 72 73 65 66 74 62 The parameter of interest is the mean size μ in this population. The sample is an SRS of size n = 4 drawn from the population. Software can be used to generate an SRS. Alternatively, because the companies are labeled 0 to 9, a single random digit from Table B chooses one company for the sample.

(a) Find the mean of the 10 sizes in the population. This is the population mean μ.

(b) Input the 10 sizes in Minitab or Excel. Refer to the Appendix of Chapter 3 to see how to use each of these software programs to generate an SRS. Alternatively, you can use Table B to draw an SRS of size 4 from this population. Draw an SRS using software or Table B and write the four sizes in your sample and calculate the mean x of the sample sizes. This statistic is an estimate of μ.

(c) Repeat this process 10 times using software or using different parts of Table B.

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 μ?