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A researcher wants to estimate the mean IQ score for a population of high school students....

A researcher wants to estimate the mean IQ score for a population of high school students. How many students will she have to select for the IQ tests if she wants 95% confidence the sample mean is within 3 IQ points of the population mean? Assume the population standard deviation is 15.

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Answer #1

Solution :

Given that,

Population standard deviation = \sigma = 15

Margin of error = E = 3

At 95% confidence level the z is,

\alpha = 1 - 95%

\alpha = 1 - 0.95 = 0.05

\alpha/2 = 0.025

Z\alpha/2 = Z0.025 = 1.96  

sample size = n = [Z\alpha/2* \sigma / E] 2

n = [ 1.96 * 15 / 3 ]2

n = 96.04

Sample size = n = 97

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