SOLUTION: You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=27.3. You would like to be

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Question 1194702: You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=27.3. You would like to be 95% confident that your estimate is within 2 of the true population mean. How large of a sample size is required?
I keep getting 264 as the answer which it says is incorrect, maybe it is my z-score?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

At 95% confidence, the z critical value is roughly z = 1.960
Use a Z table or calculator to determine this.

We're told that sigma = 27.3
The error we want is E = 2 or smaller.

Let's compute the min sample size.
n = (z*sigma/E)^2
n = (1.960*27.3/2)^2
n = 715.776516
n = 716
Always round up to the nearest whole number.
If we got something like 715.00001, then we would still round up to 716 to clear the hurdle.

Here is a short derivation of where this version of min sample size formula comes from
E = margin of error
E = z*sigma/sqrt(n)
E*sqrt(n) = z*sigma
sqrt(n) = z*sigma/E
n = (z*sigma/E)^2

Answer: 716