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=35.3σ=35.3. You would like to be 95% confident
that your estimate is within 0.1 of the true population mean. How
large of a sample size is required?

As in the reading, in your calculations:

--Use z = 1.645 for a 90% confidence interval

--Use z = 2 for a 95% confidence interval

--Use z = 2.576 for a 99% confidence interval.

Answer #1

Solution :

Population standard deviation = = 35.3

margin of error = E = 0.1

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 2

sample size = n = [Z/2* / E] 2

n = [2 * 35.3 / 0.1]2

n = 498436

Sample size = n = 498436

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