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 98% 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 70 52 37 39 59 30 31 30

Wife 64 56 30 48 71 42 43 21

Step 1 of 4: Find the mean of the paired differences, 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 98% confidence interval. Round your answers to one decimal place.

Answer 1

The statistical software output for this problem is :

Paired T confidence interval:
μ_D = μ₁ - μ₂ : Mean of the difference between Husband and Wife
98% confidence interval results:

Difference	Mean	Std. Err.	DF	L. Limit	U. Limit
Husband - Wife	-3.375	3.2838213	7	-13.219737	6.469737

The mean of the paired differences = -3.4

critical value = 2.998

The standard deviation of the paired differences is 9.3

The 98% confidence interval is : -13.2 to 6.5