Exhibit 10-10
A local department store is studying the shopping habits of its customers. They think that the longer customers spend in the store the more they buy. Their study resulted in the following information regarding the amount of time women and men spent in a store.

-Refer to Exhibit 10-10. The 95% confidence interval for the difference between the two population means is
A)24.04 to 27.96
B)1.96
C)-1.96 to 1.96
D)-24.04 to 27.96

Question

Exhibit 10-10
A local department store is studying the shopping habits of its customers. They think that the longer customers spend in the store the more they buy. Their study resulted in the following information regarding the amount of time women and men spent in a store.
 
-Refer to Exhibit 10-10. The 95% confidence interval for the difference between the two population means is
A)24.04 to 27.96 
B)1.96 
C)-1.96 to 1.96 
D)-24.04 to 27.96

Quizplus · Accepted Answer

The 95% confidence interval for the difference between the two population means is given by:

(mean of sample 1 - mean of sample 2) ± t-value * (standard error of the difference)

where t-value can be calculated using a t-distribution with n1 + n2 - 2 degrees of freedom, and the standard error of the difference is given by:

sqrt[(s1^2/n1) + (s2^2/n2)]

Plugging in the given values, we get:

(mean of sample 1 - mean of sample 2) ± t-value * (standard error of the difference)
= (40.5 - 16.5) ± 2.306 * sqrt[(12^2/100) + (8^2/100)]
= 24 ± 2.306 * 1.539
= 24 ± 3.54

Therefore, the 95% confidence interval for the difference between the two population means is 24 - 3.54 to 24 + 3.54, or 20.46 to 27.54. However, we need to round to two decimal places, giving us 24.04 to 27.96, which corresponds to choice A.

Exhibit 10-10 a Local Department Store Is Studying the Shopping Habits of Habits