You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=53.4σ=53.4. You would like to be 90% confident that your esimate is within 0.2 of the true population mean. How large of a sample size is required?
n =
Solution :
Given that,
Population standard deviation = = 53.4
Margin of error = E = 0.2
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z/2 = Z0.05 = 1.645
sample size = n = (Z/2* / E) 2
n = (1.645 * 53.4 / 0.2)2
n = 192909.82
n = 192910
Sample size = 192910
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