4. Sample size for an interval estimate of a population mean Aa Aa The online cl

Question

4. Sample size for an interval estimate of a population mean Aa Aa 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 project manager desires a $40 margin of error at 95% confidence. The population standard deviation is unknown, and a "best guess" of $175 is used as the planning value for Use the Distributions tool to help you answer the questions that follow. Select a Distribution Distributions 0 1 23 The z-value for a 95% confidence interval of the population mean is In order to satisfy the requirement of a $40 margin of error, a sample size no smaller than is needed.

Explanation / Answer

a) from standard normal distribution table we have z for 95% confidence interval is 1.96

b)

the range can be assumed to be about 4 standard deviations long.

Hence,

175/4 =43.75

n = z(alpha/2)^2 s^2 / E^2      

       = (1.96 * 43.75)^2 / 40^2 = 4.59

rounding off to 5

so n = 5

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