SOLUTION: Determine the necessary sample size for a confidence interval around a sample mean: Set the confidence level at 95%; the population standard deviation, even though unknown, is ass

Question 1182109: Determine the necessary sample size for a confidence interval around a sample mean: Set the confidence level at 95%; the population standard deviation, even though unknown, is assumed to be 6.5 (in the same units of measure as the sample mean), and the desired margin of error is 1.5. What sample size would you need to use to accomplish this result?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
error=half-interval=z*sigma/sqrt(n)
1.5=1.96*6.5/sqrt(n)
sqrt(n)=1.96*6.5/1.5
=8.49
sample size is 72.1 or 73
Because the std dev is not known a t-value with df=72 is 1.996
re-calculate using that value and (1.996*6.5/1.5)^2=74.81 or sample size 75.
If the population std dev is unknown, and a sample sd is used, this is a t-test. This wasn't clear here, although if one needed to mention the mean and sd have the same units, I would assume a z-test. It is worth asking that question.

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