1. From Simulations to the Central Limit Theorem

2. Parameter: A number describing a characteristic of the population
(usually unknown)
Statistic: A number describing a characteristic of a sample.
Let’s review some vocabulary

3. In Inferential Statistics we use the value of a sample statistic to estimate a parameter value.
POPULATION: ALL Montgomery College students and estimate their mean height

4. We want to estimate the mean height of MC students.
Will x-bar be equal to mu? What if we had selected another sample? What is the variability of the x-bars about the mean mu?
What if we get another sample, will x-bar be the same?

5. What does the x-bar distribution look like?

6. How do we investigate the behavior of x-bar?
WHY WORRIED ABOUT PROBABILITIES? In inferential statistics we test claims about population means by using probabilities

7. Graph the x-bar distribution and find its mean and standard deviation

8. Simulation Rolling a fair die and recording the outcome randInt(1,6)
Press MATH
Go to PRB
Select 5: randInt(1,6)

9. Rolling a die n times and finding the mean of the outcomes.
Mean(randInt(1,6,10)
Press 2nd STAT
Right to MATH
Select 3:mean
Press MATH
Right to PRB
5:randInt(

10. Rolling a die n times and finding the mean of the outcomes.
The Central Limit Theorem in action
Meaning of FAIR –SHAPE, MEAN, ST.DEV = Think now on the possible x-bars if n = 2, if n = 10

11. Simulation
Roll a die 5 times and record the number of ONES obtained:
randInt(1,6,5)
Press MATH
Go to PRB
Select 5: randInt(1,6,5)

12. The Central Limit Theorem in action
Roll a die 5 times, record the number of ONES obtained.
Do the process n times and find the mean number of ONES obtained.
The Central Limit Theorem in action

13. The Central Limit Theorem in action

19. Use website APPLETS to simulate proportion problems