Two taled discrete hypothesis test question (OCR S2).

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BecauseFP
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Given that this is a two-tailed test, why does it matter if you use > or <? Surely one will just look for 0.975 and the other 0.025?
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poorform
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Because I think they are using the binomial distribution to carry out the test. I don't think n is large enough/p is small enough to carry out the test by approximating with the normal also.
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BecauseFP
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(Original post by poorform)
Because I think they are using the binomial distribution to carry out the test. I don't think n is large enough/p is small enough to carry out the test by approximating with the normal also.
Not using normal I understand, it's punishing the use of <7 that I don't.
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BecauseFP
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Oh, wow, I misspelled "tailed" in the title, is there anyway to change that?
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rayquaza17
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(Original post by BecauseFP)
Not using normal I understand, it's punishing the use of <7 that I don't.
But the binomial distribution isn't symmetric, which is what your argument for 0.975 and 0.025 relies on.
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BecauseFP
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(Original post by rayquaza17)
But the binomial distribution isn't symmetric, which is what your argument for 0.975 and 0.025 relies on.
Now I just feel stupid, but how do we know to use >?
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rayquaza17
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(Original post by BecauseFP)
Now I just feel stupid, but how do we know to use >?
We are using greater than or equal to, not >?


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BecauseFP
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(Original post by rayquaza17)
We are using greater than or equal to, not >?


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I mean how do we know to use > as opposed to <?
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rayquaza17
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(Original post by BecauseFP)
I mean how do we know to use > as opposed to <?
I'll reply back to this tomorrow night if that's okay? Haven't got the time to check through my notes to write you a proper answer right now.


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BecauseFP
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(Original post by rayquaza17)
I'll reply back to this tomorrow night if that's okay? Haven't got the time to check through my notes to write you a proper answer right now.


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No problem, my attempt to explain this to myself is little more than this MSPaint confusion.
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username1732133
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(Original post by BecauseFP)
No problem, my attempt to explain this to myself is little more than this MSPaint confusion.
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It should look more like this I think.
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BecauseFP
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(Original post by BuryMathsTutor)
It should look more like this I think.
Fair enough, but why is it that when we have a value of 7, we use >7? Why is <7 wrong?

I understand that once we start talking about rejection regions, it's quickly obvious that you must be >8 or <0, but in terms of working with p values, why is this the case?
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username1732133
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(Original post by BecauseFP)
...why is it that when we have a value of 7, we use >7? Why is <7 wrong?
Could you try to make this question clearer?
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BecauseFP
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(Original post by BuryMathsTutor)
Could you try to make this question clearer?
I was referring back to the original post. The question gives us a value of 7 to work with "Seven of the 12 people said that they preferred blue", and our hypotheses are H0: P=1/3 and H1 P is not equal to 1/3. So how do we know that the right thing to do is consider P(>7), rather than anything to do with P(<7)?
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username1732133
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(Original post by BecauseFP)
I was referring back to the original post. The question gives us a value of 7 to work with "Seven of the 12 people said that they preferred blue", and our hypotheses are H0: P=1/3 and H1 P is not equal to 1/3. So how do we know that the right thing to do is consider P(>7), rather than anything to do with P(<7)?
You should be asking yourself, is 7 or more that unlikely, given H0?

In precise terms, is P(X \ge 7) &lt; 0.025 ? And of course the answer to that question is no.

Alternatively you can find the critical region and check to see whether or not 7 is in the critical region.
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BecauseFP
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(Original post by BuryMathsTutor)
You should be asking yourself, is 7 or more that unlikely, given H0?

In precise terms, is P(X \ge 7) &lt; 0.025 ? And of course the answer to that question is no.

Alternatively you can find the critical region and check to see whether or not 7 is in the critical region.
As I've said, once you consider critical regions it's not an issue, but what about
P(X \le 7) &lt; 0.975 ?

While I completely understand that P(X \le 7)  \neq 1 - P(X \ge 7) I fail to see why the < case is wrong.
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username1732133
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(Original post by BecauseFP)
As I've said, once you consider critical regions it's not an issue, but what about
P(X \le 7) &lt; 0.975 ?

While I completely understand that P(X \le 7)  \neq 1 - P(X \ge 7) I fail to see why the < case is wrong.
I see. Whilst showing that P(X \le 7) &gt; 0.975 is equivalent to showing that P(X \ge 8) &lt; 0.025 it doesn't show that P(X \ge 7) &gt; 0.025.
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BecauseFP
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(Original post by BuryMathsTutor)
I see. Whilst showing that P(X \le 7) &gt; 0.975 is equivalent to showing that P(X \ge 8) &lt; 0.025 it doesn't show that P(X \ge 7) &gt; 0.025.
But why is it that what we need to show is P(X \ge 7) &gt; 0.025?

Again, I must stress that I can easily see this when we're talking about critical regions and that 7 plain and simply isn't in the critical region, but how do we know to use \ge 7?
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BecauseFP
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(Original post by rayquaza17)
I'll reply back to this tomorrow night if that's okay? Haven't got the time to check through my notes to write you a proper answer right now.


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Did you find anything?
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rayquaza17
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(Original post by BecauseFP)
Did you find anything?
Nah. I haven't done examples where it was worded this way, and I don't really understand statistics well enough to make an educated guess as to why they do this.

Sorry.
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