ISUCKATCHEMISTRY
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#1
what is a test statistic?
The book says "The result of the experiment or the statistic, that is calculated from the sample is called the test statistic."
Not sure what that means.
I don't understand.
And what do the critical values mean!
Help if you can, thanks!
Is there any specimen papers that are for AS only, all the ones i find are a mixture of as and a2.
For the new specimen A level maths, thanks.
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Kevin De Bruyne
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#2
Report 3 years ago
#2
(Original post by ISUCKATCHEMISTRY)
what is a test statistic?
The book says "The result of the experiment or the statistic, that is calculated from the sample is called the test statistic."
Not sure what that means.
I don't understand.
And what do the critical values mean!
Help if you can, thanks!
Is there any specimen papers that are for AS only, all the ones i find are a mixture of as and a2.
For the new specimen A level maths, thanks.
A test statistic is a value obtained from the data you have and it gives you an estimate of what you're trying to estimate

Let's say you want to test a coin and whether p(heads) = 0.5 and you throw it 100 times. Then your test statistic is the number of heads / 100. This is because it's an estimate for the proportion of coin throws that are heads which is what we're interested in

So if we got 58 heads then the test sstaistic is 58/100 = 0.58 and we test whether it is different from 0.5. Because even if p(heads) is 0.5, 59 heads is still not unlikely.

Try it yourself, with 10 coin flips. You know p(heads) = 0.5 so you'd expect 5 heads, but can get 4,6 or 3,7 or even 2,8. But if you get 0 or 10 then something is very wrong with your assumption. And that's what the critical region is - it's the values of the test statistic which are deemed unlikely by the null hypothesis, because if anything very unlikely (less than 0.05 probability happens) then something is usually wrong. For example, 10/10 heads or 0/10 heads would suggest something is wrong with the coin, and that you'd only get this if p(heads) = 0.5 around 1 in 2^10 times. See your textbook for how to calculate the critical region, but it's the range of values of the test statistic which suggest something is wrong
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