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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

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

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