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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 $00$. 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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    [Chi-squared test](http://en.wikipedia.org/wiki/Chi-squared_test).2011-10-27
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    (Assuming that your Wikipedia problem was that you couldn't find the right article, that is).2011-10-27
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    @wircho The $\chi^2$-test in part b is the Pearson's $\chi^2$-test ([wiki](http://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test)-article). This is slightly more technical than the page Henning links to2011-10-27
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    Thanks Sasha! But how does one prove that this is a Pearson's $\chi^2$ test? I don't see any relation.2011-10-27
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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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