Problem 4 (Testing for equality of spread). Healthy vs. Failed Firms contd. Recall that in Problem 1 part (1.2) above you ran the hypothesis test for difference in means assuming that the population standard deviation for both the groups is identical. Let's test that assumption. (4.1) Easy. What statistic would you use to test that the population standard deviations for the two types of firms is equal? Clearly write out the hypothesis and calculate the relevant statistic. (4.2) Moderate. What are the exact degrees of freedom associated with the F-statistic in this case? (4.3) Challenging. Test the hypothesis in part (4.1) at the 5% level. Does your conclusion justify the assumption made in Problem 1