You and a Friend Want to Estimate the Proportion of Undergraduates

Multiple Choice

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.