Chapter 8.2, Problem 25E

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 populations have equal variances, you can construct a confidence interval for μ₁ − μ₂, as shown below.

$({\bar{x}}_1-{\bar{x}}_2)-t_c\hat{\sigma }•\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}<{\mu }_1-{\mu }_2<({\bar{x}}_1-{\bar{x}}_2)+t_c\hat{\sigma }•\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$

$where\hat{\sigma }=\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}andd.f.=n_1+n_2-2$

In Exercises 25 and 26, construct the indicated confidence interval for μ₁ − μ₂. Assume the populations are approximately normal with equal variances.

25. Family Doctor To compare the mean number of days spent waiting to see a family doctor for two large cities, you randomly select several people in each city who have had an appointment with a family doctor. The results are shown at the left. Construct a 90% confidence interval for the difference in mean number of days spent waiting to see a family doctor for the two cities. (Adapted from Merritt Hawkins)

TABLE FOR EXERCISE 25