You and a friend want to estimate the proportion of undergraduates at a college who favor eliminating evening exams. Your friend will choose a simple random sample of 250 students. If you choose a simple random sample of 1000 students, your sample proportion
A) will have the same mean and the same standard deviation.
B) will have smaller bias and the standard deviation will be 1/4 as large.
C) will have smaller bias and the standard deviation will be 1/2 as large.
D) will have the same mean and the standard deviation will be 1/4 as large.
E) will have the same mean and the standard deviation will be 1/2 as large.

Question

Quizplus · Accepted Answer

The sample proportion from a larger sample size will have a smaller bias because it is more likely to represent the true population proportion. However, the standard deviation will be reduced by a factor of the square root of the sample size, which means that for a sample size of 1000 (compared to 250), the standard deviation will be 1/2 as large. Therefore, choice E is the correct answer.

You and a Friend Want to Estimate the Proportion of Undergraduates