Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 75.1 . You would like to be 99% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Do not round mid-calculation.

*n* =

Answer #1

Solution :

Given that,

standard deviation = =75.1

Margin of error = E = 1

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z_{/2}
= 2.576

sample size = n = [Z_{/2}*
/ E] ^{2}

n = ( 2.576* 75.1 / 1 )^{2}

n =37426

Sample size = n =37426

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