As we mentioned on page 403, the following relationship holds between hypothesis tests and confidence intervals: For a two-tailed hypothesis test at the significance level α, the null hypothesis H0: μ1 = μ2 will be rejected in favor of the alternative hypothesis Ha: μ1 ≠ μ2 if and only if the (1 − α)-level confidence interval for μ1 − μ2 does not contain 0. In each case, illustrate the preceding relationship by comparing the results of the hypothesis test and confidence interval in the specified exercises.
a. Exercises 10.71 and 10.77
b. Exercises 10.76 and 10.82