I solved part (a) of this problem but I don't understand what a $\chi^2$ test is in part (b) (Wikipedia did not help me):
Let $X_1,\ldots,X_n$ be a random sample from a distribution with pdf $f(x)=\theta x^{\theta-1}$, for $0
and $\theta>0$. We want to test the hypothesis $H_0:\theta\leq5$ against $H_1:\theta>5$. (a) Show that the likelihood-ratio test rejects $H_0$ when $-\sum\log X_i$ is too small.
(b) Show that the test in (a) is equivalent to a $\chi^2$ test.