# What does a 95% versus a 99% confidence interval mean for a given estimate?

Oct 30, 2015

It is the probability value of an inferenced population mean likely to fall with in a given range.

#### Explanation:

From the sample mean $\overline{x}$ we try to estimate the population mean $\mu$

$\mu = \overline{x} \pm z . S E$

The upper limit of the mean is given by
$\mu = \overline{x} + z . S E$

The lower limit of the mean is given by
$\mu = \overline{x} - z . S E$

Where -

$\mu$ is population Mean
$\overline{x}$ is sample Mean
$S E$ standard error
$z$ is the critical value. Its value is defined by the confidence level.

If the confidence level is 95% $z$ value is $1.96$
If the confidence level is 99% $z$ value is $2.58$

With an increase in confidence level the chance of population mean to fall within the range is high.

You must understand the confidence level doesn't stand for accuracy in estimate.

Higher the confidence level less is the accuracy.