The following relationship holds between hypothesis tests and confidence intervals for one-mean t-procedures: For a two-tailed hypothesis test at the significance level α, the null hypothesis H0: μ = μ0 will be rejected in favor of the alternative hypothesis Ha: μ = μ0 if and only if μ0 lies outside the (1 − α)-level confidence interval for μ.
In each case, illustrate the preceding relationship by obtaining the appropriate one-mean t-interval (Procedure 8.2 on page 328) and comparing the result to the conclusion of the hypothesis test in the specified exercise.
a. Exercise 9.101
b. Exercise 9.104