STEPS FOR TESTING DIFFERENCE BETWEEN SAMPLE STATISTIC AND POPULATION PARAMETER (OR
SOME LARGER GROUP FROM WHICH THE SAMPLE IS DRAWN)
This is where you have knowledge of the population mean and perhaps the population standard
deviation. You have a sample mean and you want to know how different it is from the larger group from
which it was taken.
So for example you might know the national average age and you want to know if KY residents are
younger in age from the national average (this indicates a one tail test).
IF you know the population mean and the population standard deviation then you use the following
formula to calculate Z.
𝑍
=
𝑌
�
− 𝜇
𝑦
𝜎
𝑦
√𝑁
�
Once you calculate Z, you need to decide what alpha level you are using, 0.01 or 0.05 for instance. (In
exam questions I’ll give you that information.)
Look the Z score up in Appendix B.
If your Z is negative you will need to take the absolute value of it
(make it positive).
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 Spring '11
 Heberle
 Statistics, Standard Deviation, 60 degrees

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