I'm reading the introductory statistics and get stuck at chi square test for variances. Like the image shown below, the alternative hypothesis is that
$σ^2 < 7.2^2$
. But if we plug this inequality into the formula for the calculation of chi square value $(n-1)*S^2/σ^2$ (S is the sample standard deviation), the result is supposed to be $χ^2 > (n-1)*S^2/7.2^2 = 5.67$, which suggests that this is a upper sided test. However, the truth is that this is a lower sided test. Is there anything wrong? Thanks!
Best Answer
I know it's late but I think your problem is that you wonder why for a given alpha like 0.05, your test statistic is on the right side and 1-alpha on the left side. because in chi square distribution area you have under the curve is being computed from right not left(unlike t-test for example)