Population Variance

(This Hypothesis Test Works For All Sample Sizes)

The procedure for this process is presented in the flow chart on the previous page.   

The three main choices for the null hypothesis and the alternative hypothesis are the following:

Null Hypothesis    Versus      Alternative Hypothesis

H_o:  s² = constant                 vs.                        H_a:  s²  ¹constant  (Two-Tailed)

H_o:  s²  ³ constant                 vs.                        H_a:  s² < constant (Left-Tailed)

H_o:  s² < constant                 vs.                        H_a:  s² > constant (Right-Tailed)

The critical number is dependent on which of the above tests (two-tailed, left-tailed and right-tailed) the problem involves.  For a chi-squared distribution, the following table is needed :

[Degrees of Freedom (df) = n -1 ]

Chi-Squared Table

The main difference in the procedure occurs in the step that deals with the test statistic.  The test statistic for the population variance is the following:

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