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 = 19.8 \\) years, based on a previous report. should the sample be obtained from one movie at one theater? the required sample size is 1062. (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 simple random 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 cluster 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 a population parameter (in this case, the mean age of movie - patrons), the sample should be representative. A sample from one movie at one theater is likely to be a convenience sample. Convenience samples are prone to bias as they do not represent the entire population of movie - patrons. For example, different movies (e.g., a children's movie vs. an adult - oriented drama) at different theaters (e.g., in a college town vs. a retirement community) will have different age distributions. A simple random sample of the broader population (all movie - patrons) is a better choice as it gives each member of the population an equal chance of being selected, reducing the potential for bias.

Answer:

A. 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.