Exhibit 10-7
In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered.
-Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is
A)0.078 to 1.922
B)1.922 to 2.078
C)1.09 to 4.078
D)1.078 to 2.922

Question

Exhibit 10-7
In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. 
-Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is
A)0.078 to 1.922 
B)1.922 to 2.078 
C)1.09 to 4.078 
D)1.078 to 2.922

Quizplus · Accepted Answer

Using the formula for a confidence interval for the difference of means, we have:

(point estimate) +/- (critical value) * (standard error of difference)

Point estimate = x̄1 - x̄2 = 20.50 - 19.00 = 1.50
Standard error of difference = sqrt [ (s1^2/n1) + (s2^2/n2) ] = sqrt [ (3.00^2/15) + (2.50^2/20) ] = 0.6876
Critical value with 95% confidence and 33 degrees of freedom (n1 - 1 + n2 - 1) is 2.03

Plugging in the values, we get:

1.50 +/- 2.03 * 0.6876

This gives us a range of (0.08, 2.92). Rounding to two decimal places, the answer is (0.08 to 1.92), which corresponds to choice A.

Exhibit 10-7 In Order to Estimate the Difference Between the Average Hourly