Question

find the sample size needed to estimate the mean age of movie patrons such that it can be said with 98% confidence that the sample mean is within 2.5 years of the population mean. assume that ( sigma = 19.5 ) years, based on a previous report. should the sample be obtained from one movie at one theater?
the required sample size is 331. (round up to the nearest integer.)
should the sample be obtained from one movie at one theater?
a. 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.
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.
c. 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.
d. the sample should be obtained from one movie at one theater, because that sample is representative of the population

Explanation:

When obtaining a sample to estimate the mean age of movie patrons, a sample from one movie at one theater is likely to be biased. Different movies attract different age - groups (e.g., a children's movie will have a younger audience, and a classic film screening may have an older audience). A simple random sample of the broader population (all movie patrons across different movies, theaters, times, etc.) is more likely to be representative. Cluster sampling groups the population into clusters and then randomly selects some clusters. Stratified sampling divides the population into strata and samples from each stratum. But for a general estimate of the mean age of movie patrons, a simple random sample of the broader population is the most straightforward way to avoid the bias of a single - movie - single - theater sample.

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.