## Hypothesis Testing for the Variance or Standard Deviation

The sampling distribution for the variance of a normaldistribution with variance isgiven by This means that if a random sample of size istaken from a normally distributed population with variance thenthe random variable hasthe distributionwith degreesof 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 fora two tailed test OR that either OR fora one tailed test.

3. Find the test statistic Comparethis with the values of -two tailed test – or -if is  if is -from the tables.

4. Reject ifthe test statistic falls into any of the shaded regions in thediagram below, else do not reject  Example: Conduct a hypothesis test at the 95% level to testwhether the variance of the population from which this sample istaken

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  