Download The Mean and Standard Deviation of š

7.2 - The Mean and Standard Deviation of 
The relation
 = 
*** See example 7.4, p. 319
Mean of the variable 
For samples of size n, the mean of all possible sample means equal the mean
of the population.
 = 
The relation between  and 
*** See example 7.5, p. 320
Standard Deviation of the Variable 
For samples of size n, the standard deviation of all possible sample means
equals the population standard deviation divided by the square root of the
sample size.
 =

n
Note
When sampling is done without replacement from a finite population the
approximate formula is
N n 
 =
N 1
n
where n is the sample size and N is the population size.
When the sample size is small relative to the population size (that is,
n  0.05N), as happens in most practical applications, there is little
difference between sampling with and without replacement and the answers
from the two formulas are “close”. In this book we’ll be using the first
formula with the understanding that the answers may be only
approximate.
*** See example 7.6, p. 322
*** do # 7.30, p. 324
*** do # 7.32, p. 324
*** do # 7.34, p. 324
Standard Error (SE) of the Sample Mean: 
The standard deviation of  determines the amount of sampling error to be
expected when a population mean is estimated by a sample mean. This
sampling error gets smaller as the sample size increases.
▪ The larger the sample size, the smaller is the standard deviation of .
▪ The smaller the standard deviation of , the more closely the possible
values of  cluster around the mean of .