Question

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was four minutes. Use that as a planning value for the standard deviation in answering the following questions. a. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 69 seconds, what sample size should be used? Assume 95% confidence. b. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.

Answer 1

Please note for the following problem, I have converted everything in seconds.

A)

The following information has been provided:

The critical value for the significance level α=0.05 is ​=1.96. The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:

Therefore, the sample size needed to satisfy the condition , and it must be an integer number, we conclude that the minimum required sample size is n = 47

B)

The following information has been provided:

The critical value for the significance level α=0.05 is The following formula is used to compute the minimum sample size required to estimate the population mean \muμ within the required margin of error:

Therefore, the sample size needed to satisfy the condition , and it must be an integer number, we conclude that the minimum required sample size is n=62.

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