A recent survey asked a sample of 1010 people if they were baseball fans; 454 people in the sample said Yes. Assuming there is no bias, one can be 95 percent confident that the percent of all adults who are baseball fans is approximately between:
A) 41 percent and 49 percent.
B) 42 percent and 48 percent.
C) 40 percent and 50 percent.
D) 37 percent and 53 percent.
E) 34 percent and 56 percent.

Question

Quizplus · Accepted Answer

Using a 95% confidence interval, we can use the formula:

Sample proportion +/- Margin of error = Confidence interval

where Sample proportion = 454/1010 = 0.4495

Margin of error = 1.96 * √(0.4495(1-0.4495)/1010) = 0.034

Confidence interval = 0.4495 +/- 0.034 = (0.4155, 0.4835)

Converting to percentages, we get (41.55%, 48.35%), which falls within the range of option B. Therefore, the best choice is B) 42 percent and 48 percent.

A Recent Survey Asked a Sample of 1010 People If