Summary Stats 188 chapter 7 notes

CHAPTER 7 SAMPLING DISTRIBUTIONS

SAMPLING DISTRIBUTIONS OF THE MEAN
The possible
>
sampling distribution of the mean is the
sampling distribution of all sample means calculated


from all possible samples of a
given size .




02

If ~
( v4.02 ) then ~ ill
,
n and 2 = 5C -


m


O
n




* since the population mean (µ ) and the mean of the
sampling distribution Of the mean are both equal ,




the sample mean (E) Is said to be an unbiased estimate of the population mean cut .




As the sample size ( ) increases the standard error ( Osi O ) of the distribution of
n
sampling
= n
,




the mean decreases




standard error of mean : Ox = o

n




> SAMPLING FROM NORMALLY DISTRIBUTED POPULATIONS :

◦
If sampling is done from a population that IS
normally distributed with mean i t and standard deviation


0
,
then regardless of the sample size
,
n
,
the sampling distribution of the mean is normally
°
distributed ,
with mean Mx = it and standard error of the mean OI = n




o
finding Z for the
sampling distribution


of the mean :




2- =
MI

Oi


=
µ

o
.




n




◦
Finding for the
sampling distribution of the mean




0
=
µ t Z n