A local planning commission is interested in finding out what proportion of its city's residents is opposed to constructing a new baseball stadium in the downtown area. A random sample of 1870 residents is obtained, and 41.2 percent of them are opposed to the stadium.
A 95 percent confidence interval was created for the proportion of the city's residents who are opposed to constructing a new baseball stadium in the downtown area. Decreasing the sample size will:
A) result in a narrower interval because there will be less information.
B) result in a narrower interval because the margin of error will decrease.
C) result in a wider interval because the margin of error will increase.
D) result in a wider interval because the average scores will change.
E) not affect the confidence interval at all.

Question

Quizplus · Accepted Answer

Decreasing the sample size will result in a wider interval because the margin of error will increase. The margin of error is directly proportional to the square root of the sample size. Therefore, decreasing the sample size will increase the margin of error, resulting in a wider confidence interval.

A Local Planning Commission Is Interested in Finding Out What