The online clothing retailer e-Parel is conducting a study to estimate the avera
ID: 3150661 • Letter: T
Question
The online clothing retailer e-Parel is conducting a study to estimate the average size of the orders placed by visitors to its website. The study researcher desires a $50 margin of error at 99% confidence. The population standard deviation is unknown, so a best guess is used as the planning value for a. e-Parel estimates that the smallest order in the population of orders placed at its website is $20 (the price of the least expensive item in its catalog), and the largest order is $720 (three times the price of the most expensive item in its catalog). A rough approximation of the population standard deviation is To satisfy the requirement for the margin of error, a sample size no smaller than is needed.Explanation / Answer
The range can be assumed to be about 6 standard deviations long.
Hence,
6*sigma = 720-20
sigma = 700/6 = 116.6666667 [ANSWER, ROUGH APPROXIMATION]
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Note that
n = z(alpha/2)^2 s^2 / E^2
where
alpha/2 = (1 - confidence level)/2 = 0.005
Using a table/technology,
z(alpha/2) = 2.575829304
Also,
s = sample standard deviation = 116.6666667
E = margin of error = 50
Thus,
n = 36.12332596
Rounding up,
n = 37 [ANSWER]
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