The results of a recent poll on the preference of shoppers regarding two products are shown below. At 95% confidence, the margin of error is
A) .064.
B) .044.
C) .0225.
D) .025.

Question

The results of a recent poll on the preference of shoppers regarding two products are shown below.  ​ At 95% confidence, the margin of error is
A) .064. 
B) .044. 
C) .0225. 
D) .025.

Quizplus · Accepted Answer

To find the margin of error, we use the formula:
Margin of Error = Z* * (sqrt(p*(1-p))/sqrt(n))
where Z* = the critical value for the desired level of confidence (in this case, 1.96 for 95% confidence), p = the proportion of respondents who prefer Product A, and n = the sample size.

Using the data from the poll: 
p = 243/500 = 0.486
n = 500

Margin of Error = 1.96 * (sqrt(0.486*(1-0.486))/sqrt(500)) = 0.044

Therefore, the margin of error is 0.044, which corresponds to answer choice B.

The Results of a Recent Poll on the Preference of Shoppers