Hypothesis Testing for the Variance or Standard Deviation
The sampling distribution for the variance of a normaldistribution with varianceisgiven by
This means that if a random sample of sizeistaken from a normally distributed population with variancethenthe random variablehasthedistributionwithdegreesof freedom.
To perform a hypothesis test for the hypothesis
Is the population normal?
State the null hypothesis– that-and the alternative hypothesis–that fora two tailed test OR that eitherORfora one tailed test.
Find the test statistic Comparethis with the values of-two tailed test – or-ifisifis-from thetables.
Rejectifthe 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
is equal to 1.
The test statistic is
We do not reject