Left-Tailed Hypothesis Tests and CIs. If the assumptions for a nonpooled t-interval are satisfied, the formula for a (1 − α)-

level upper confidence bound for the difference, μ1 − μ2, between two population means is

(x¯1 − x¯2) + tα ·

(s2 1 /n1) + (s2 2 /n2).

For a left-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 upper confidence bound for μ1 − μ2 is less than or equal to 0. In each case, illustrate the preceding relationship by obtaining the appropriate upper confidence bound and comparing the result to the conclusion of the hypothesis test in the specified exercise.

a. Exercise 10.81

b. Exercise 10.82