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use the given data to find the minimum sample size required to estimate a population...

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surfer3 | Valedictorian

Posted May 30, 2012 at 7:13 PM via web

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use the given data to find the minimum sample size required to estimate a population proportion or percentage

Margin of error: 0.005, confidence level: 99%, p and q unknown

 

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted May 31, 2012 at 4:37 AM (Answer #1)

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Unless the population proportion is very skewed, you can use p=.5 and q=.5

E=.005; confidence level of 99% implies `z_(alpha/2)=2.58` and

`E=z_(alpha/2)sqrt((pq)/n)`

`.005=2.58sqrt((.5*.5)/n)`

`.0019379845=sqrt((.25)/n)`

`266256=n/.25`

n=66564

Thus to get an error of 1/2% with 99% confidence, you need a sample size of at least 66564.

** You may question the ability to use p=q=.5 As long as the population isn't very divided, the numbers are approximately the same. Using 40% and 60% yields 266256*.24=63901. Even 70%-30% gives 266256*.21=55914, so the use of 50-50 is justified. **

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