The manager in charge of concessions at an NFL football stadium is interested in estimating the mean dollars that are spent per person attending the games. A pilot sample of n = 50 people has revealed a sample mean and standard deviation of $12.35 and $2.35 respectively. He wishes to estimate the population mean within ± $0.20 of the true mean and wishes to have a confidence level of 95 percent. Given this, he needs to sample an additional 481 people.

Question

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To find the required sample size, the formula for the sample size in estimating a population mean is used: n = (Z * σ / E)^2, where Z is the Z-score for the desired confidence level (1.96 for 95%), σ is the standard deviation, and E is the margin of error. Plugging in the values: n = (1.96 * 2.35 / 0.20)^2 ≈ 531. Since 50 people have already been sampled, an additional 481 people are needed.

The Manager in Charge of Concessions at an NFL Football