To compare the mean ages of male and female participants in a 10K race, you randomly select several ages from both sexes. The results are shown below. Construct a 95% confidence interval for the difference in mean ages of male and female participants in the race.

When the sampling distribution for x̅₁ - x̅₂ is approximated by a t-distribution and the populations have equal variances, you can construct a confidence interval for μ₁ - μ₂, as shown below.

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

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Sample Statistics for Ages of 10K Race Participants Females Males X2 = 41 years s2 = 14.4 years 12 X1 = 41 years s1 = 13.7 years П2 nị = 20 (X1 – X2) – tô • V n1 < µ1 - M2 < (x1 – x2) + te • п2 V n1 п2 (п1 1)sĩ + (n2 – 1)sź and d.f. = n1 + n2 - 2 where ở = пу + ng — 2