Shake Shack at the mall is a popular destination with long wait times. Suppose we wish...

Shake Shack at the mall is a popular destination with long wait times. Suppose we wish to estimate the wait time for customers at peak dinner time. Assume a previous random sample of size 30 was taken and the sample mean was found to be 14.82 minutes with a sample standard deviation of 4.13 minutes. How large a sample should they take to estimate the true mean wait time to be within 1.2 minutes at the 95% confidence interval?

Expert Solution

Given ME = 1.2, Sigma(Standard Deviation) = 4.13, Alpha() = 0.05

The Zcritical at Alpha() = 0.01 is 1.96

The ME is given by :

ME = Z critical * Std Deviation(SD) / Sqrt(n)

Squaring both sides we get: (ME)² = (Z critical)² * (SD)²/n

Therefore n = (Zcritical * SD/ME)² = (1.96*4.13/1.2)² = 45.5

Therefore n = 46 (Taking it to the next whole number)

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orchestra answered 2 years ago

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Shake Shack at the mall is a popular destination with long wait times. Suppose we wish...

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