Question 6.17

6.17 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 1 to 10.

301

Company 1 2 3 4 5 6 7 8 9 10
Size 82 62 80 58 72 73 65 66 74 62

The parameter of interest is the mean size in this population. The sample is an SRS of size drawn from the population. Software can be used to generate an SRS.

  1. Find the mean of the 10 sizes in the population. This is the population mean.
  2. Use now software to make an SRS of size 3.
    • Excel users: A simple way to draw a random sample is to enter “=RANDBETWEEN(1,10)” in any cell. Take note of the number that represents company and record in another column the corresponding size. Hit the F9 key to change the random entry. If you get a repeat, hit the F9 again. Do this until you get three distinct values.
    • JMP users: Enter the size values in a data table. Do the following pull-down sequence: Table → Subset. In the drag-down dialog box named Initialize Data, pick Random option. Choose the bullet option of Random - sample size and enter “3” in its dialog box and then click OK. You will find an SRS of three company sizes in a new data table.
    • Minitab users: Enter the size values in column one (c1) a data table. Do the following pull-down sequence: Calc → Random Data → Sample from Samples. Enter “3” in the Number of rows to sample, type “c1” in the From columns box, and type “c2” in the Store samples in box, and then click OK. You will find an SRS of three company sizes in c2.

    With your SRS calculate the sample mean . This statistic is an estimate of .

  3. Repeat this process nine more times. Make a histogram of the 10 values of You are constructing the sampling distribution of Is the center of your histogram close to ?

6.17

(a) (b) Software, answers will vary. (c) Software, answers will vary.