The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

Two taled discrete hypothesis test question (OCR S2).

June 2012.png
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?

Scroll to see replies

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.
Reply 2
Avatar for BecauseFP
BecauseFP
OP
2
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.
Reply 3
Avatar for BecauseFP
BecauseFP
OP
2
Oh, wow, I misspelled "tailed" in the title, is there anyway to change that?
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.
Reply 5
Avatar for BecauseFP
BecauseFP
OP
2
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 >?
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 >?


Posted from TSR Mobile
(edited 8 years ago)
Reply 7
Avatar for BecauseFP
BecauseFP
OP
2
Original post by rayquaza17
We are using greater than or equal to, not >?


Posted from TSR Mobile


I mean how do we know to use > as opposed to <?
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. :frown:


Posted from TSR Mobile
Reply 9
Avatar for BecauseFP
BecauseFP
OP
2
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. :frown:


Posted from TSR Mobile


No problem, my attempt to explain this to myself is little more than this MSPaint confusion.
I am totally sane.jpg
Original post by BecauseFP
No problem, my attempt to explain this to myself is little more than this MSPaint confusion.
I am totally sane.jpg


It should look more like this I think.
tsr260515.png24.8KB
Reply 11
Avatar for BecauseFP
BecauseFP
OP
2
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?
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?
Reply 13
Avatar for BecauseFP
BecauseFP
OP
2
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)?
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≥7)<0.025P(X \ge 7) < 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.
Reply 15
Avatar for BecauseFP
BecauseFP
OP
2
Original post by BuryMathsTutor
You should be asking yourself, is 7 or more that unlikely, given H0?

In precise terms, is P(X≥7)<0.025P(X \ge 7) < 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≤7)<0.975P(X \le 7) < 0.975 ?

While I completely understand that P(X≤7)≠1−P(X≥7)P(X \le 7) \neq 1 - P(X \ge 7) I fail to see why the < case is wrong.
(edited 8 years ago)
Original post by BecauseFP
As I've said, once you consider critical regions it's not an issue, but what about
P(X≤7)<0.975P(X \le 7) < 0.975 ?

While I completely understand that P(X≤7)≠1−P(X≥7)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≤7)>0.975P(X \le 7) > 0.975 is equivalent to showing that P(X≥8)<0.025P(X \ge 8) < 0.025 it doesn't show that P(X≥7)>0.025P(X \ge 7) > 0.025.
Reply 17
Avatar for BecauseFP
BecauseFP
OP
2
Original post by BuryMathsTutor
I see. Whilst showing that P(X≤7)>0.975P(X \le 7) > 0.975 is equivalent to showing that P(X≥8)<0.025P(X \ge 8) < 0.025 it doesn't show that P(X≥7)>0.025P(X \ge 7) > 0.025.


But why is it that what we need to show is P(X≥7)>0.025P(X \ge 7) > 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 ≥7\ge 7?
Reply 18
Avatar for BecauseFP
BecauseFP
OP
2
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. :frown:


Posted from TSR Mobile

Did you find anything?
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. :frown:

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you