You want to determine the true mean strength of a new concrete mix with a precision of 50 psi at a confidence level of 99%. If you assume the population standard deviation is 100 psi, what size sample should you use?

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- Dec 8th 2008, 12:40 AMccdelia7Sample Size
You want to determine the true mean strength of a new concrete mix with a precision of 50 psi at a confidence level of 99%. If you assume the population standard deviation is 100 psi, what size sample should you use?

- Dec 9th 2008, 07:26 PMmeymathis
Well the standard deviation of a sample mean is the population standard deviation divided by the square root of the sample size.

In other words, if $\displaystyle \sigma$ is the population mean of some random variable $\displaystyle X$, and suppose you are going to take samples of size $\displaystyle N$. The sample mean, $\displaystyle \bar{X}$ is another random variable. (It's mean is the population mean, but that is not relevant here).

$\displaystyle \sigma_{\bar{X}} = \sigma/\sqrt{N}$

where $\displaystyle \sigma_{\bar{X}}$ is the standard deviation of $\displaystyle \bar{X}$.

You know 2 of the 2 variables in that equation so have at it!