Question

The U.S. Census Bureau collects data on the ages of married people. Suppose that eight married couples are randomly selected and have the ages given in the following table. Determine the 90% confidence interval for the true mean difference between the ages of married males and married females. Let d=(age of husband)−(age of wife). Assume that the ages are normally distributed for the populations of both husbands and wives in the U.S.:

Husband: 75 41 62 38 53 27 59 46

Wife: 63 29 67 29 49 29 53 57

Step 1 of 4:

Find the mean of the paired differences, d‾‾ (line goes above d). Round your answer to one decimal place.

Step 2 of 4:

Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 3 of 4:

Find the standard deviation of the paired differences to be used in constructing the confidence interval. Round your answer to one decimal place.

Step 4 of 4:

Construct the 90% confidence interval. Round your answers to one decimal place.

Answer 1

1)

dbar =3.1
2)

Critical value of t are -1.895 and 1.895.

3)

sd = 8.4

4)

sample mean, xbar = 3.1
sample standard deviation, s = 8.4
sample size, n = 8
degrees of freedom, df = n - 1 = 7

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.895

ME = tc * s/sqrt(n)
ME = 1.895 * 8.4/sqrt(8)
ME = 5.6

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (3.1 - 1.895 * 8.4/sqrt(8) , 3.1 + 1.895 * 8.4/sqrt(8))
CI = (-2.5 , 8.7)