Question

A sociologist is studying trends related to marriage in the United States. She polls an initial sample of 20 couples in the US to find their difference in age. The mean difference in age ?̅ is 1.875 years. The standard deviation ?? is 3.055 years. Assuming the data is composed of a proper simple random sample, find the 95% confidence interval for the mean difference in age between men and women in a couple.

Answer 1

95% confidence interval for the mean difference in age between men and women in couple

d bar - t​​​​​​a/2​​​​​​*( Sd /√ n ) <  D < d bar + t​​​​​​a/2*( Sd/√n)

For a = 0.05 , d.f = n -1 = 19

t​​​​​​a/2, n -1  = t​​​​​​0.05,19 = 2.09

1.875 -2.09*(3.055/√20) < D < 1.875 + 2.09*(3.055/√20)

0.447 < D < 3.0303