The sampling distribution for the variance of a normal distribution with varianceis given by

This means that if a random sample of sizeis taken from a normally distributed population with variancethen the random variablehas thedistribution withdegrees of freedom.

To perform a hypothesis test for the hypothesis

1. Is the population normal?

2. State the null hypothesis – that- and the alternative hypothesis– that for a two tailed test OR that eitherORfor a one tailed test.

3. Find the test statistic Compare this with the values of- two tailed test – or- ifisifis- from thetables.

4. Rejectif the test statistic falls into any of the shaded regions in the diagram below, else do not reject

Example: Conduct a hypothesis test at the 95% level to test whether the variance of the population from which this sample is taken

3,4,3,4,5,6,2,3,4,5

is equal to 1.

Null Hypothesis,

Alternative Hypothesis,

The test statistic is

and

We do not reject