Exhibit 10-10
The results of a recent poll on the preference of shoppers regarding two products are shown below.
-Refer to Exhibit 10-10. 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 10-10
The results of a recent poll on the preference of shoppers regarding two products are shown below. 
-Refer to Exhibit 10-10. 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 95% confidence interval for the difference between the two population proportions, we need to calculate the point estimate and the standard error. The point estimate is the difference between the sample proportions: 0.38 - 0.4 = -0.02. The standard error is calculated as:

sqrt((p1*(1-p1)/n1) + (p2*(1-p2)/n2))
= sqrt((0.38*(1-0.38)/200) + (0.4*(1-0.4)/200))
= 0.049

Using a t-distribution with degrees of freedom equal to (n1-1) + (n2-1) = 398, and a confidence level of 95%, we lookup the t-value of 1.96. The 95% confidence interval is then:

-0.02 ± 1.96(0.049)
= -0.024 to 0.064

Therefore, the best choice is A.

Exhibit 10-10 the Results of a Recent Poll on the Preference of Preference