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Discussion (WK3)
Question 1:
As a sample size approaches infinity, how does the student’s t distribution compare to the
normal z distribution? When a researcher draws a sample from a normal distribution, what can
one conclude about the sample distribution? Explain.
Zdistribution is used to approximate a normal distribution of data.
Is normally distributed with mean 0 and variance 1, as the sample mean is normally distributed with mean
μ
and
standard error
where σ
2
is population variance and “n” is the sample size (when “n” is large or greater than 30).
We use Zdistribution to test a certain hypothesis, when population variance is known.
On the other hand, tdistribution can be defined as:
This differs from Z as the exact standard deviation is replaced by the sample variance which is a random variable
and thus this has a Student's tdistribution. Therefore, to test a certain hypothesis, we use tdistribution, when
population variance is unknown and hence we replace it by the sample variance S
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This note was uploaded on 08/29/2011 for the course EC 315DLB taught by Professor Randallbarcus during the Fall '10 term at Park.
 Fall '10
 RandallBarcus

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