You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 36.9 . You would like to be 98% confident that your estimate is within 0.2 of the true population mean. How large of a sample size is required?
Solution :
Given that,
Population standard deviation = = 36.9
Margin of error = E = 0.2
At 98% confidence level the z is,
= 1 - 98%
= 1 - 0.98 = 0.02
/2 = 0.01
Z/2 = 2.326
sample size = n = [Z/2*
/ E] 2
n = [ 2.326 * 36.9 / 0.2]2
n = 184167.14
Sample size = n = 184168
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