One reason for being conservative when determining the number of degrees of freedom to use with the tdistribution is the possibility that the population variances might be unequal. Extremely different values cause a lowering in the number of df used. Repeat Exercise 10. 79 using theoretical normal distributions of N(100, 9) and N(120, 27) and both sample sizes of 8. Check all three properties of the sampling distribution: normality, its mean value, and its standard error. Describe in detail what you discover. Do you think we should be concerned about the choice of df? Explain.