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# Stat question watch

1. Now I have a question
they stated that population variance is assumed to be the same as the sample one.

but the markscheme uses the t-test because it says the sample size is small

but is it wrong if I use the z test?

Thanks~
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2. (Original post by akk713)
Now I have a question
they stated that population variance is assumed to be the same as the sample one.

but the markscheme uses the t-test because it says the sample size is small

but is it wrong if I use the z test?

Thanks~
the Normal distribution (Z test) should only be used as an approximation when the sample size is 30 or over, because it is a continuous distribution, and you will get a sampling error if you use it for small discrete values.
3. (Original post by 4Ed)
the Normal distribution (Z test) should only be used as an approximation when the sample size is 30 or over, because it is a continuous distribution, and you will get a sampling error if you use it for small discrete values.
So I should use the t-test regardless whether I know the variance or not?
I thought for any sample size, if the variance is known, you can still use the z test?!
4. (Original post by akk713)
So I should use the t-test regardless whether I know the variance or not?
I thought for any sample size, if the variance is known, you can still use the z test?!
read http://mathworld.wolfram.com/Student...tribution.html for the definition of the t-test.
if the sample is small and discrete, you can't model it using a normal distribution - but as the sample size increases, the student-t graph approximates to a normal distribution, and that's why it cant be used in this case... the sample size is too small.

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