Chapter 8.2, Problem 23E

Constructing Confidence Intervals for μ₁ − μ₂ When the sampling distribution for ${\bar{x}}_1-{\bar{x}}_2$ is approximated by a t-distribution and the population variances are not equal, you can construct a confidence interval for μ₁ − μ₂, as shown below.

$({\bar{x}}_1-{\bar{x}}_2)-t_c\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}<{\mu }_1-{\mu }_2<({\bar{x}}_1-{\bar{x}}_2)+t_c\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$

where d, f, is the smaller of n₁ − 1 and n₂ − 1

In Exercises 23 and 24, construct the indicated confidence interval for μ₁ − μ₂. Assume the populations are approximately normal with unequal variances.

23. 10K Race To compare the mean finishing times of male and female participants in a 10K race, you randomly select several finishing times from both sexes. The results are shown at the left. Construct an 80% confidence interval for the difference in mean finishing times of male and female participants in the race. (Adapted from Xact)

TABLE FOR EXERCISE 23