# Estimation from Sample Data:

• Feb 1st 2009, 08:34 AM
loriemomof2
Estimation from Sample Data:
A sample random sample of 30 has been collected from a population for which it is known that σ= 17.0. The sample mean has been calculated as
342.0, and the sample standard deviation is s=14.9. Need some help to construct and interpret the 95% and the 99% confidence intervals for the population mean.
• Feb 1st 2009, 09:38 AM
Constatine11
Quote:

Originally Posted by loriemomof2
A sample random sample of 30 has been collected from a population for which it is known that σ= 17.0. The sample mean has been calculated as
342.0, and the sample standard deviation is s=14.9. Need some help to construct and interpret the 95% and the 99% confidence intervals for the population mean.

The sample mean is normally distributed with mean equal to the population mean $\displaystyle \mu$ and sd $\displaystyle s=\sigma/\sqrt{N}$ where $\displaystyle N$ is the sample size.

So the required confidence intervals should be:

$\displaystyle [m-z_{p}s,\ m+z_{p}s]$

where $\displaystyle z_p$ is the critical value for a standard normal distribution so that $\displaystyle p(|z|<z_p)=p$ which you look up in a table. But you should have memorised that $\displaystyle z_{0.95}=1.96$ because it occurs so often.

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