Estimation from Sample Data:

**loriemomof2** · February 1st 2009, 08:34 AM

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.

**Constatine11** · February 1st 2009, 09:38 AM

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 $\mu$ and sd $s=\sigma/\sqrt{N}$ where $N$ is the sample size.

So the required confidence intervals should be:

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

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

.

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