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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.

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    Can you show us what you did for part a) it might be easier to see what the problem is if we can see where you got to and how.2013-02-08

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