A recent survey of 174,745 randomly selected U.S. adults studied the importance of religion to Americans in each state.
The survey found that nationwide 40 percent said that they were very religious. But in New Hampshire, the least religious state, only 20 percent answered that they were "very religious." The sample included 1000 respondents from New Hampshire. The margin of error in a 95 percent confidence interval for the proportion of all adults who are very religious is:
A) larger for New Hampshire than for the nation.
B) the same for New Hampshire and for the nation.
C) smaller for New Hampshire than for the nation.
D) random, so one can't make a comparison.

Question

Quizplus · Accepted Answer

The margin of error for a proportion in a sample is influenced by the sample size and the proportion itself. Given the same confidence level, the margin of error is larger for smaller samples (1000 in New Hampshire vs. 174,745 nationwide) and when the proportion is closer to 50%. Since the sample size for New Hampshire is significantly smaller than the nationwide sample, the margin of error for New Hampshire's estimate will be larger.

A Recent Survey of 174,745 Randomly Selected U