The chi-square distribution was described on page 517 as a family of distributions. Let’s investigate these distributions and observe some of their properties.

a. Use the MINITAB commands that follow and generate several large random samples of data from various chi-square distributions. Use df values of 1, 2, 3, 5, 10, 20, and 80 (and others if you wish).

Choose: Calc  Random Data  ChiSquare Enter: Generate: 1000 rows of data Store in column(s): C1 Degrees of freedom: df Use Stat  Basic Statistics  Display Descriptive Statistics to calculate the mean and median of the data in C1. Use Graph  Histogram to construct a histogram of the data in C1.

b. What appears to be the relationship between the mean of the sample and the number of degrees of freedom?

c. How do the values of the mean, median, and mode appear to be related? Do your results agree with the information on page 517?

d. Have the computer generate samples for two additional degrees of freedom df  120 and 150. Describe how these distributions seem to be changing as df increases.