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Hypothesis testing

When you're doing a two tailed test i.e. h1: p cannot equal 0.5 do you find P(X<x) or P(X>x) or is either fine? My book says if either of them is less than a (significance level) then reject the null hypothesis, is that correct?
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@Zacken
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Zacken
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Original post by mp_x
When you're doing a two tailed test i.e. h1: p cannot equal 0.5 do you find P(X<x) or P(X>x) or is either fine? My book says if either of them is less than a (significance level) then reject the null hypothesis, is that correct?


If your significance level is n%n\% then you need to find P(X≤x)≤n2%P(X \leq x) \leq \frac{n}{2} \% and P(X≥x)≤n2%P(X \geq x) \leq \frac{n}{2} \% (equality signs need to be adjusted for discrete stuff)

This is a really good video explaining two tailed tests: http://www.examsolutions.net/maths-revision/statistics/hypothesis-tests/binomial/examples/example-5.php
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Original post by Zacken
If your significance level is n%n\% then you need to find P(X≤x)≤n2%P(X \leq x) \leq \frac{n}{2} \% and P(X≥x)≤n2%P(X \geq x) \leq \frac{n}{2} \% (equality signs need to be adjusted for discrete stuff)

This is a really good video explaining two tailed tests: http://www.examsolutions.net/maths-revision/statistics/hypothesis-tests/binomial/examples/example-5.php


Do you need to find both? My book says OR
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Original post by mp_x
Do you need to find both? My book says OR


Your critical values are given by doing both, yeah. There are some times when you do the other non-critical values method where you can just pick the smaller tail, but if I personally just stick to doing both all the time.
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Original post by Zacken
Your critical values are given by doing both, yeah. There are some times when you do the other non-critical values method where you can just pick the smaller tail, but if I personally just stick to doing both all the time.


Thank you! When using the non-critical values method why would you pick the lower tail and not the upper?
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Original post by mp_x
Thank you! When using the non-critical values method why would you pick the lower tail and not the upper?


You wouldn't! There's be some scenarios where you'd pick the lower and some where you'd pick the higher, it's not always the lower one. You'd need to pick whichever gives you the smallest (or biggest I don't remember since I don't use this method myself) probability since then the other would would necessarily be bigger (or smaller).

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