Find the critical z (alpha divided by two) values if the confidence level is 99%

We are asked to find the critical value(s) for a 99% confidence level:

Since we are using z we may be testing a claim about the population mean (with the population standard deviation known) or testing a claim about a population proportion among other possible tests.

Assuming that the test is two-tailed (e.g. we are interested in whether the sample mean differs from the population mean as opposed to is less than the population mean),...

We are asked to find the critical value(s) for a 99% confidence level:

Since we are using z we may be testing a claim about the population mean (with the population standard deviation known) or testing a claim about a population proportion among other possible tests.

Assuming that the test is two-tailed (e.g. we are interested in whether the sample mean differs from the population mean as opposed to is less than the population mean), there are two critical values.

To compute the values we take 1 minus the confidence level -- thus 1-.99=.01. Since there are two critical regions, equal in area by symmetry, we divide the answer by 2 to get .005.

Now we look in a standard normal table for the z-score that corresponds to an area of .005 (or to an area of 1-.005=.995 as the z-value will be the same with opposite sign) to find `z~~ pm 2.58 ` . Note that a graphing calculator or statistics package can give a more precise answer such as ` z~~ pm 2.575829303 ` which could also be calculated using calculus.)

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The critical values are approximately z=-2.58 and z=2.58

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These critical values define critical regions -- if a test statistic falls in the critical region we would reject the null hypothesis.