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

  1. Is the population normal?

  2. State the null hypothesis– that-and the alternative hypothesis–that fora two tailed test OR that eitherORfora one tailed test.

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

  4. 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.

Null Hypothesis,

Alternative Hypothesis,

The test statistic is


We do not reject

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