Download Sampling Means

Chapter 9.3:
Sample Means
Mr. Lynch
AP Statistics
Sample Means
 Sample Proportions … answer questions like …
“What % of Americans watch Survivor?”
 “What % of the adult population attended
church last week?”
 What if our variable is “quantitative” … as in :
 “Income of a household”
 Lifetime of a brake-pad”
 Blood pressure of a patient”
 We use what is called a SAMPLE MEAN

BULL MARKET OR BEAR MARKET?
OBSERVATIONS
Averages are less
variable than
individual
observations!
Averages are more
“normal” than
individual
observations!
Sampling Distribution Mean
and Standard Deviation
 Sampling Distribution Mean
:
 Sampling Distribution Standard Deviation
 Sampling Distribution from a Normal Population :
:
EXAMPLE 9.10:
YOUNG WOMEN’S HEIGHTS
 N(64.5,2.5); n = 10
 Sampling Distribution Mean?
 Sampling Distribution Standard Deviation?
EXAMPLE 9.11:
(MORE ON) YOUNG WOMEN’S HEIGHTS
 “What is the probability that a
randomly selected individual
woman is taller than 66.5
inches?”
 “What is the probability that the
mean height of an SRS of 10
randomly selected women is
greater than 66.5 inches?”
Sample Distribution versus
Population Distribution
The Central Limit Theorem
 Draw an SRS of size n from ANY
POPULATION WHATSOEVER with
mean
and standard deviation .
When n is large, the sampling
distribution of the sample means
is
close to the Normal Distribution with:
Example 9.12
SKEWED POPULATIONS
Exponential Distributions
EXAMPLE 9.13:
SERVICING AIRCONDITIONERS
 “What is the probability that the
average maintenance exceeds
50 minutes on 70 units?
