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 80%80% confidence interval for the true mean difference between the ages of married males and married females. Let d=(age of husband)−(age of wife)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 31 48 49 58 60 43 46 59 Wife 2828 60 59 55 55 39 35 60

Step 1 of 4 : Find the mean of the paired differences, d‾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 80% confidence interval. Round your answers to one decimal place. lower endpoint:= ______ and upper endpoint:=_____

Answer 1

1)

Husband wife dbar

31 28 3

48 60 -12

49 59 -10

58 55 3

60 55 5

43 39 4

46 35 11

59 60 -1

mean of paired differences = 0.3

2)

Critical value = +/-1.4149

3)

standard deviation of paired differences = 6.7

4)

CI = dbar +/- t *(s/sqrt(n))

= 0.3 +/- 1.4149 *(6.7/sqrt(8))

= (-3.1,3.7)

lower endpoint = -3.1

Upper endpoint = 3.7