Use a computer to demonstrate the truth of the theory presented in this section.
a. The underlying assumptions are “the populations are normally distributed,” and while conducting a hypothesis test for the equality of two standard deviations, it is assumed that the standard deviations are equal. Generate very large samples of two theoretical populations: N(100, 20) and N(120, 20). Find graphic and numerical evidence that the populations satisfy the assumptions.
b. Randomly select 100 samples, each of size 8, from both populations and find the standard deviation of each sample.
c. Using the first sample drawn from each population as a pair, calculate the F_-statistic. Repeat for all samples. Describe the sampling distribution of the 100 F_-values using both graphic and numerical statistics.
d. Generate the probability distribution for F(7, 7), and compare it with the observed distribution of F_. Do the two graphs agree? Explain.