# What is a $\chi^2$-test?

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 $0<x\leq1$ 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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– Henning Makholm Oct 27 '11 at 20:07
(Assuming that your Wikipedia problem was that you couldn't find the right article, that is). – Henning Makholm Oct 27 '11 at 20:13
@wircho The $\chi^2$-test in part b is the Pearson's $\chi^2$-test (wiki-article). This is slightly more technical than the page Henning links to – Sasha Oct 27 '11 at 20:25
Thanks Sasha! But how does one prove that this is a Pearson's $\chi^2$ test? I don't see any relation. – wircho Oct 27 '11 at 21:37
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. – Magpie Feb 8 '13 at 0:03