A Gallup Poll asked, "What is your favorite Summer Olympics event?" Of the people asked, 27 percent said, "swimming." Here is what Gallup says about the accuracy of this poll:
The results are based on telephone interviews with a sample of 1007 national adults, aged 18 years and older. For results based on the total sample of national adults, one can say with 95 percent confidence that the maximum error attributable to sampling and other random effects is plus or minus 3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.
Suppose 500 people in the sample of 1007 adults were women. Gallup asked these 500 women, "What is your favorite Summer Olympic event?" Thirty-five percent said swimming was their favorite. Gallup gave a margin of error for this result. Applying the quick method, one finds that the margin of error for 95 percent confidence changes when the sample size drops from 1007 to 500, from:
A) 4.5 percent to 3.2 percent.
B) 3.2 percent to 4.5 percent.
C) 3 percent to 1.5 percent.
D) 3 percent to 6 percent.

Question

Quizplus · Accepted Answer

The margin of error for a sample of 1007 is 3 percentage points at 95% confidence. When the sample size reduces to 500, the margin of error increases. To calculate the new margin of error, we use the formula:

new margin of error = old margin of error/square root of (new sample size/old sample size)

Plugging in the values, we get:

new margin of error = 3%/square root of (500/1007)
new margin of error = 3.2%

Therefore, the margin of error increases from 3% to 3.2% when the sample size drops from 1007 to 500, which is option B.

A Gallup Poll Asked, "What Is Your Favorite Summer Olympics