The variable has a chi-square distribution if the population variance has a normal distribution. The degrees of freedom are n-1. We can use this to test the population variance under certain conditions
Testing is done in the same manner as before. Remember, all hypothesis testing is done under the assumption the null hypothesis is true.
If you solve the test statistic formula for the population variance, you get:
Note, the left-hand endpoint of the confidence interval comes when the right critical value is used
and the right-hand endpoint of the confidence interval comes when the left critical value is used.
This is because the critical values are in the denominator and so dividing by the larger critical
value (right tail) gives the smaller endpoint.