Question

find the sample size needed to estimate the mean age of movie patrons such that it can be said with 90% confidence that the sample mean is within 1 year of the population mean. assume that \\( \sigma=19.4 \\) years, based on a previous report. should the sample be obtained from one movie at one theater?
the required sample size is 1019. (round up to the nearest integer.)
should the sample be obtained from one movie at one theater?
oa. the sample should not be obtained from one movie at one theater, because that sample could be easily biased. instead, a stratified sample of the broader population should be obtained.
ob. the sample should not be obtained from one movie at one theater, because that sample could be easily biased. instead, a simple random sample of the broader population should be obtained.
oc. the sample should be obtained from one movie at one theater, because that sample is representative of the population.
od. the sample should not be obtained from one movie at one theater, because that sample could be easily biased. instead, a cluster sample of the broader population should be obtained.

Explanation:

A sample from one movie at one theater is likely to be biased. People who watch a particular movie at a specific theater may not represent the entire population of movie patrons. A simple random sample of the broader population (not limited to one movie and one theater) is a better approach as it has a higher chance of being representative. Stratified sampling (Option A) is used when there are distinct subgroups in the population, but the problem doesn't mention such subgroups. Cluster sampling (Option D) involves dividing the population into clusters and sampling some clusters, which is not indicated here.

Answer:

B. The sample should not be obtained from one movie at one theater, because that sample could be easily biased. Instead, a simple random sample of the broader population should be obtained.