Question

In: Statistics and Probability

The U.S. Census Bureau collects data on the ages of married people. Suppose that eight married...

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)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 43 63 65 30 33 33 66 22
Wife 34 66 72 26 25 24 63 23

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 98% confidence interval. Round your answers to one decimal place.

Solutions

Expert Solution

Step1:

difference=d=Husband -wife

9 -3 -7 4 8 9 3 -1

mean(d)=sum/total=22/8=2.75=2.8

mean=2.8

Step2:

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

df=n-1=8-1=7

alpha=0.02

t critical=

=T.INV.2T(0.02,7)

=2.997952

T critical=2.998

t=2.998

Step3:

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

Sd=

d dbar d-dbar (d-dbar)^2
9 2.75 6.25 39.0625
-3 2.75 -5.75 33.0625
-7 2.75 -9.75 95.0625
4 2.75 1.25 1.5625
8 2.75 5.25 27.5625
9 2.75 6.25 39.0625
3 2.75 0.25 0.0625
-1 2.75 -3.75 14.0625
total 249.5

Sd=sqrt(249.5/8-1)

Sd=5.970164

Sd=6

Sd=6

Step4:

98% confidence interval for difference in means

dbar-t*sd/'sqrt(n),sbar+t*sd/sqrt(n)

2.75-2.997952*5.970164/sqrt(8),2.75+2.997952*5.970164/sqrt(8)

-3.577992, 9.077992

-3.6,9.1

98% confidence interval for difference in means is

-3.6 and 9.1

orchestra answered 2 years ago
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