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.
Solution :
Given that,
Population standard deviation = = 15
Margin of error = E = 3
At 95% confidence level the z is,
= 1 - 95%
= 1 - 0.95 = 0.05
/2 = 0.025
Z_{/2} = Z_{0.025} = 1.96
sample size = n = [Z_{/2}* / E] ^{2}
n = [ 1.96 * 15 / 3 ]^{2}
n = 96.04
Sample size = n = 97
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