Unbalanced sample sizes are a factor in determining the number of degrees of freedom for inferences about the difference between two means. Repeat Exercise 10. 79 using theoretical normal distributions of N(100, 20) and N(120, 20) and sample sizes of 5 and 20. 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 when using unbalanced sample sizes? Explain.