3.7 Which is more accurate? The Pew Research Center Report entitled “How Americans value public libraries in their communities,” released December 11, 2013, asked a random sample of 6224 Americans aged 16 and older, “Have you used a Public Library in the last 12 months?” In the entire sample, 30% said Yes. But only 17% of those in the sample over 65 years of age said Yes. Which of these two sample percents will be more accurate as an estimate of the truth about the population?
(a) The result for those over 65 is more accurate because it is easier to estimate a proportion for a small group of people.
(b) The result for the entire sample is more accurate because it comes from a larger sample.
(c) Both are equally accurate because both come from the same sample.
(d) We cannot determine this, because we do not know the percentage of those in the sample 65 years of age or younger who said Yes.