Refer to Exercise 12.11. Assume that 2 1 = 2 2 = 2. The table values used to implement a

Chapter 12, Problem 12.12

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Refer to Exercise 12.11. Assume that 2 1 = 2 2 = 2. The table values used to implement a test of hypothesis or construct a confidence interval depend, for small samples, on the number of degrees of freedom associated with the estimates for 2 or 2 D. a Assuming two independent samples, each of size n, and that 2 1 = 2 2 = 2, how many degrees of freedom are associated with the estimator for the common variance 2? b Assuming a matched-pairs experiment consisting of n pairs of observations, how many degrees of freedom are associated with the estimator of 2 D? c Assume that all of the assumptions necessary to implement the independent samples t procedures are satisfied and that we want to find a 95% confidence interval for the difference in means. What are the values oft.025 used to construct confidence intervals for the difference in means based on the independent samples and matched-pairs experiments if n = 5? If n = 10? If n = 30? d If all of the assumptions necessary to implement the independent samples t procedures are satisfied, identify a possible disadvantage to implementing a matched-pairs experiment rather than taking independent samples