Aa Aa E 4. Sample size for an interval estimate of a population mean The Cinema

Question

Aa Aa E 4. Sample size for an interval estimate of a population mean The Cinema Advertising Council is conducting a study to estimate the average number of minutes moviegoers spend at the theater before the previews begin. The study researcher desires a 2-minute margin of error at 90% confidence The population standard de is unknown, so a best guess is used as the planning value for a. The council viation estimates that the smallest amount of time spent at the theater in the population of moviegoers is -5 minutes (a moviegoer arrives 5 minutes late), and the largest amount of time spent at the theater is 25 minutes. A rough approximation of the population standard deviation is Use the Distributions tool to help to answer the quest n that f WS ollo Standard Normal Mean 30.0 Standard Deviation 1.0 is needed. To satisfy the requirement for the margin of error, a sample size no smaller than

Explanation / Answer

A rough estimate of population standard deviation is

range=max-min value=25-(-5)=25+5=30

standard deviation =30/4=7.5

Not all data is normally distributed and bell curve shaped. But most data is well behaved enough that going two standard deviations away from the mean captures nearly all of the data. We estimate and say that four standard deviations is approximately the size of the range, and so the range divided by four is a rough approximation of the standard deviation.

min sample size=

n=( zsigma/E)2

=(1.645*7.5/2)2

z alpha/2 for 90%=1.645

  =38.05

Min sample size=38

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