Question

ch 8* the pew research centers report entitled \how americans value public libraries in their communities,\ released december 11, 2013, asked a random sample of 6224 americans aged 16 and over, \have you used a public library website 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?

options:

• both are equally accurate because both come from the same sample.
• the result for those over 65 is more accurate because it is easier to estimate a proportion for a small group of people.
• the result for the entire sample is more accurate because it comes from a larger sample.

Explanation:

In sampling, the accuracy of a sample proportion as an estimate of the population proportion is related to the sample size. Larger sample sizes generally lead to more accurate estimates (less sampling error). The entire sample has a larger size (6224) compared to the subgroup of those over 65 (which is a subset of the 6224, so smaller). The first option is wrong because even from the same overall sample, subgroup samples are smaller. The second option is wrong as smaller groups (samples) have more sampling error, not less. So the result from the larger (entire) sample is more accurate.

Answer:

The result for the entire sample is more accurate because it comes from a larger sample.