1. Chapter 9.3: Sample Means
Mr. Lynch
AP Statistics

2. 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

3. BULL MARKET OR BEAR MARKET?
OBSERVATIONS
Averages are less variable than individual observations!
Averages are more “normal” than individual observations!

4. Sampling Distribution Mean and Standard Deviation
Sampling Distribution Standard Deviation :
Sampling Distribution from a Normal Population :

5. EXAMPLE 9.10: YOUNG WOMEN’S HEIGHTS
N(64.5,2.5); n = 10
Sampling Distribution Mean?
Sampling Distribution Standard Deviation?

6. 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?”

7. Sample Distribution versus Population Distribution

8. 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:

9. Example 9.12 SKEWED POPULATIONS Exponential Distributions

10. EXAMPLE 9.13: SERVICING AIRCONDITIONERS
“What is the probability that the average maintenance exceeds 50 minutes on 70 units?