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# S2 Hypothesis Testing Question Watch

1. For part ai) I'm not sure whether to find the probability X more than or equal to 9. Or do I do less than or equal to 9?

I've been confused about this many times, can someone please explain which one I use for which question and why? If it wasn't two tailed then is it the same thing? Really want to clear this up now as its my first exam

Thank you
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2. The result you'd expect to see if the teacher were right is 20% of 20, which is 4. What we have is clearly much more, so we're expecting the teacher's hypothesis to be wrong, or at least to squeak through being correct.

We want a two-tailed test, because there are two ways in which the teacher can be wrong: there's "fewer" and "more" people than expected could have read the Deano, so we need to take both sides into account. Therefore we need P(X >= 9 given that 20% of people read the Deano) to be less than 2.5% in order to reject the null hypothesis.
The reason we used "X >= 9" was that we're really calculating P(X is more extreme than we measured it, given that H0 is true); the way X is more extreme in this case is to make it larger. If it had been observed that one student (instead of 9) read the Deano, we'd use P(X <= 1). Also, if the teacher had predicted "20% or fewer of the students read the Deano", then it would be a one-tailed test and we'd use 5%. https://en.wikipedia.org/wiki/Two-tail
3. (Original post by Smaug123)
The result you'd expect to see if the teacher were right is 20% of 20, which is 4. What we have is clearly much more, so we're expecting the teacher's hypothesis to be wrong, or at least to squeak through being correct.

EDIT: I've worked out why I was wrong in saying "you need a two-tailed test", and have fixed my paragraph.

We want a one-tailed test, because there is only one "extreme direction" in which the teacher can be wrong: there's no way to have a negative number of people who read the Deano, so the only "extreme" is "more people read the Deano". Therefore we need P(X >= 9 given that 20% of people read the Deano) to be less than 5% in order to reject the null hypothesis.
The reason we used "X >= 9" was that we're really calculating P(X is more extreme than we measured it, given that H0 is true); the way X is more extreme in this case is to make it larger. If it had been observed that one student (instead of 9) read the Deano, we'd use P(X <= 1). Also, if the teacher had predicted "20% or fewer of the students read the Deano", then it would still be a one-tailed test and we'd use 5%, but if we were measuring something normally distributed, like height, then we'd have two "extreme" directions and hence would use the two tails. https://en.wikipedia.org/wiki/Two-tail
But i thought two tailed is when its either equal to or not equal to?
In the mark scheme it says = or not equal to and then part ii possible values for X are x=0 or [9,20] there is a value above and below 9 doesn't it mean two tailed?
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4. (Original post by .raiden.)
But i thought two tailed is when its either equal to or not equal to?
In the mark scheme it says = or not equal to and then part ii possible values for X are x=0 or [9,20] there is a value above and below 9 doesn't it mean two tailed?
Ah no, I've been stupid - I was right the first time! I'll fix my post - it is indeed two-tailed (I saw something in the mark scheme that made me think it was meant to be one-tailed, but I misinterpreted it.)
5. (Original post by Smaug123)
Ah no, I've been stupid - I was right the first time! I'll fix my post - it is indeed two-tailed (I saw something in the mark scheme that made me think it was meant to be one-tailed, but I misinterpreted it.)
So if the observed value is more than the expected value (mean) then we do more than but if less then less? This is the same for one tailed right?
6. (Original post by .raiden.)
So if the observed value is more than the expected value (mean) then we do more than but if less then less? This is the same for one tailed right?
That's correct in all the combinations of cases {two/one tailed, measurements >/< mean, hypothesis states "=" or "<"}, I think (though I may have got lost on the way), so I think the answer is "yes".
Someone more statsful might want to verify this? (I'm just a pure boy, I need no hypotheses…)

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