Exhibit 11-1
The results of a recent poll on the preference of shoppers regarding two products are shown below.

-Refer to Exhibit 11-1. The 95% confidence interval estimate for the difference between the populations favoring the products is
A)-0.024 to 0.064
B)0.6 to 0.7
C)0.024 to 0.7
D)0.02 to 0.3

Question

Exhibit 11-1
The results of a recent poll on the preference of shoppers regarding two products are shown below.
 
-Refer to Exhibit 11-1. The 95% confidence interval estimate for the difference between the populations favoring the products is
A)-0.024 to 0.064 
B)0.6 to 0.7 
C)0.024 to 0.7 
D)0.02 to 0.3

Quizplus · Accepted Answer

To find the confidence interval estimate for the difference between two proportions, we use the formula:

(point estimate) +/- (critical value) x (standard error)

where the point estimate is the difference between the sample proportions, the critical value is based on the level of confidence and degrees of freedom, and the standard error is calculated as:

sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)

Plugging in the values from the table, we get:

point estimate = 0.68 - 0.64 = 0.04
z critical value for 95% confidence = 1.96
standard error = sqrt(0.68(1-0.68)/500 + 0.64(1-0.64)/500) = 0.0305

Therefore, the confidence interval estimate is:

0.04 +/- 1.96 x 0.0305 = (0.024, 0.064)

Thus, the best choice is A, which represents the confidence interval estimate as -0.024 to 0.064.

Exhibit 11-1 the Results of a Recent Poll on the Preference of Preference