Hypothesis Test for the Standard Deviation σ
distpic_z.gifThe χ2 distribution is not symmetric and there is a different distribution for each sample size. Sample size determines the degrees of freedom. All χ2 values are positive.
χ2L and χ2R
For right, left or two tailed hypothesis tests, critical values of χ2 can be found in Table A-4. First compute (α ÷ 2) and 1.000 – (α ÷ 2). Look for the same area values in the column titles and look in the row for the number of degrees of freedom.
Because the χ2 distribution is asymmetric the right critical value is not equal to the left critical value, even if the level of significance and degrees of freedom are identical.
Test Statistic
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Formula for computing the test statistic for a hypothesis test of a claim about a standard deviation.