The critical value of chi-square is ______ when degrees of freedom equal 9 and α equals .05.

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

The Chi Square distribution is " the distribution of the sum of squared standard normal deviates. The degrees of freedom of the distribution is equal to the number of standard normal deviates being summed"

So for this case we have the degrees of freedom are df=9 and the significance level is [tex]\alpha=0.05[/tex]. On this case we have some possibilities.

Two tailed

If we assume that we have two tails and each one with [tex]\alpha/2 =0.025[/tex] of the area we can find the critical values with the following excel codes:

"=CHISQ.INV(0.025,9)", =CHISQ.INV(1-0.025,9)

And the critical values are:

[tex]\chi^2_{\alpha/2}=2.700[/tex]

[tex]\chi^2_{1- \alpha/2}=19.02[/tex]

Left tailed

If we assume that on the left tail of the distribution we have all the value for the significance level we can find the critical value with the following code: "=CHISQ.INV(0.05,9)". And the critical values is:

[tex]\chi^2_{\alpha}=3.33[/tex]

Right tailed

If we assume that on the right tail of the distribution we have all the value for the significance level we can find the critical value with the following code: "=CHISQ.INV(1-0.05,9)". And the critical values is:

[tex]\chi^2_{1-\alpha}=16.92[/tex]