2. Advanced Placement Statistics
Section 6.1: Simulation
EQ: How do you design a simulation to model behavior? How do you summarize the data from a simulation and use this data to answer a particular question?

3. Terms to Know:
Simulation --- model that imitates chance behavior of some variable of interest
SIMULATION MODELS
flip a coin:
two outcomes; equal
chance of occurring

4. probability of outcomes multiple of 10% use 0 to 9
other probability %’s use digits 00 to 99
*** Why not use
001 to 100?

5. Trial or Repetition --- repeated simulations
Independence --- the outcome of one event does not influence the outcome of another event
DO NOT SAY: ”NOT Dependent”

6. Outline for a Simulation:
Step 1: State problem
Step 2: State assumptions
State independence here!!
Step 3: Selection of simulation model
State model type (coin, random digits)
Define success
Define failure
Define a trial.

7. Based on this simulation, ….
Step 4: Conduct a trial
Simulate repetitions
Record results
Summarize data
State your conclusions.
Based on this simulation, ….
p #3

8. Problem:
What is the likelihood that all 10 randomly selected students at a particular university favor abolishing evening exams?

9. Assumptions:
84% of this university’s students favor abolishing evening exams.
One student’s opinion on abolishing evening exams is independent of another student’s opinion on abolishing evening exams.

10. Model:
Use a random digit table to simulate selecting 10 random students from this university and asking their opinion on abolishing evening exams.
Assign the digits 00 to 83 to represent “Yes” I favor abolishing evening exams.
Assign the digits 84 to 99 to represent “No” I do not favor abolishing evening exams.
A trial consists of reading 10 two-digit numbers, representing 10 students’ opinion. Run 5 trials.
REPETITION IS ALLOWED since the digits represent an opinion, Yes or No, not a student.

11. Conduct Trial/Record Results:
Use Line 129 on Table B. Write the digits on your notes and mark accordingly.
Random Digits “yes” “no”
TRIAL 1
TRIAL 2
TRIAL 3
TRIAL 4
TRIAL 5

12. Conclusions:
Based on this simulation, we can conclude if 10 students are selected at random, all of them, will favor abolishing evening exams 20% of the time.

13. Ex. 2: Is This Discrimination? p. 399
Set up and run a simulation to solve
this problem. Run 10 trials using a random
digit table beginning on line 105.

14. State Problem:
What is the likelihood that at least 6 out of 10 randomly selected fired sales people are 55 or older?

15. Assumptions: 24% of workers are 55 or older.
The age of one fired worker is independent of the age of another fired worker.

16. Model:
Use a random digit table to simulate randomly selecting 10 fired employees and asking them their age.
Assign the digits 00 to 23 to represent “Yes” the worker is 55 or older.
Assign the digits 24 to 99 to represent “No” the worker is younger than 55.
A trial consists of reading 10 two-digit numbers, representing 10 fired workers’ ages. Run 10 trials.
REPETITION IS ALLOWED since the digits represent a fired worker’s age, not the worker.

17. Use Line 105 on Table B. Write the digits on your notes and mark accordingly.

18. RESULTS:
Random Digits > < 55
TRIAL 1
TRIAL 2
TRIAL 3
TRIAL 4
TRIAL 5
TRIAL 6
TRIAL 7
TRIAL 8
TRIAL 9
TRIAL 10

19. Frequency of Trials with this Outcome
Number of Salespeople 55 or Older
Frequency of Trials with this Outcome 1 2 3 4 5 6 7 8 9 10 2 3 2 2

20. Conclusion:
Based on our simulation, the probability that 6 or more sales people in a randomly selected group of 10 fired sales people are 55 years old or older is _____. 0%

21. Assignment: Outline and Conduct a Simulation for Each
p #4 (Line 125) Run 5 trials; 0 to 6  shot made
7 to 9  shot missed
p #7 (Line 116) Run 10 trials; 0 to 4  girl
5 to 9 boy
#8 (Line 132) Run 10 trials; 0 to 5 AL wins
6 to 9  NL wins
#10 (Line 107) Run 10 trials; 0 to 4  girl
GET DIGIT ASSIGNMENT!