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.

When the sampling distribution for x̅₁ - x̅₂ 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.

where d.f. is the smaller of n₁ - 1 and n₂ - 1

Construct the indicated confidence interval for μ₁ - μ₂. Assume the populations are approximately normal with unequal variances.

Transcribed Image Text:

Sample Statistics for Finishing Times of 10K Race Participants Males Females X = 0.73 h 0.17 h X2 = 0.75 h 0.04 h S1 = 20 S2 n2 = 12 пy (X1 - X2) < µ1 - H2 < (x1 – x2) + п2 п2 nį П1