Download Chapter 18 – Part 2 Sampling Distribution Models for !

Chapter 18 - Part 2
Sampling Distribution Models for
y
What about

y?
Mean (Center)
y  
Expect to get on average μ
 y is unbiased for μ

What about

y?
Standard Deviation (Spread)
y 

n
As n gets larger,  y gets smaller.
 Larger samples are more accurate than
smaller samples

Example





Height of women has a normal distribution
N(66,2.5)
Sample n women.
Calculate mean height.
Repeat sampling.
What does sampling distribution of mean look
like?
What about


y?
Normal population distribution
Three conditions
1.
2.
3.
Sample must be random sample
Sample must be independent values
Sample must be less than 10% of population.

Shape is NORMAL DISTRIBUTION!

Expressed as N   ,  

n
Example




Roll a die n times
Find mean of n rolls
Repeat a lot of times.
What does distribution of mean look like?
What about


y?
Non-normal population distribution
Four conditions
1.
2.
3.
4.
Sample must be random sample
Sample must be independent values
Sample must be less than 10% of
population.
Is n is large (n  30)?
Then, the shape is NORMAL!!!
Central Limit Theorem

As the sample size n increases, the mean
of n independent values has a sampling
distribution that tends toward a normal
distribution.
  
N  ,

n

Central Limit Theorem
If the shape of the population is already
normal, then the Central Limit Theorem is
not needed.
 However, the distribution is still

  
N  ,

n
