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A random sample of 49 lunch customers was selected at a restaurant. The average amount of...

A random sample of 49 lunch customers was selected at a restaurant. The average amount of time the customers in the sample stayed in the restaurant was 40 minutes. From past experience, it is known that the population standard deviation equals 10 minutes.

a. Compute the standard error of the mean.
b. Construct a 95% confidence interval for the true average amount of time customers spent in the restaurant.
c. With a .95 probability, what sample size would have to be selected to provide a margin of error of 2.5 minutes or less?
Math   Statistics-And-Probability   
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Answer #1

(a) Given that standard deviation = 10 and sample size = 49

Apply formula

(b) By z critical table, z critical = 1.96 for 95% confidence level

Given that sample mean = 40, z critical = 1.96 and standard error (SE) = 1.4286

(c) Given that z critical = 1.96, margin of error (E) = 2.5 and standard deviation (sigma) = 10

Sample size calculation

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