Chapter 8.2, Problem 24E

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.

24. Golf To compare the mean driving distances for two golfers, you randomly select several drives from each golfer. The results are shown at the left. Construct a 90% confidence interval for the difference in mean driving distances for the two golfers.

TABLE FOR EXERCISE 24