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?

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

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

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

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.

Based on this simulation, …. Step 4: Conduct a trial Simulate repetitions Record results Summarize data State your conclusions. Based on this simulation, …. p. 398 #3

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

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.

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’ opinions. Run 5 trials. REPETITION IS ALLOWED since the digits represent an opinion, Yes or No, not a student.

Day 31 Agenda: Wed Thurs Mon Fri Tues

Conduct Trial/Record Results: Use Line 129 on Table B. Write the digits on your notes and mark them accordingly. Random Digits “yes” “no” TRIAL 1 TRIAL 2 TRIAL 3 TRIAL 4 TRIAL 5 36 75 95 89 84 68 28 82 29 13 7 3 18 63 85 43 03 00 79 50 87 27 8 2 69 05 16 48 17 87 17 40 95 17 8 2 84 53 40 64 89 87 20 19 72 45 7 3 05 00 71 66 32 81 19 41 48 73 10 0

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

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.

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

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

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.

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

Random Digits > 55 < 55 TRIAL 1 TRIAL 2 TRIAL 3 TRIAL 4 TRIAL 5 RESULTS: Random Digits > 55 < 55 TRIAL 1 TRIAL 2 TRIAL 3 TRIAL 4 TRIAL 5 TRIAL 6 TRIAL 7 TRIAL 8 TRIAL 9 TRIAL 10 95 59 29 40 07 69 97 19 14 81 3 7 1 9 60 77 95 37 91 17 29 75 95 35 2 8 68 41 73 50 13 15 52 97 27 65 85 08 95 70 67 50 21 14 74 87 3 7 82 73 95 78 90 20 80 74 75 11 2 8 1 9 81 67 65 53 00 84 38 31 48 93 60 94 07 20 24 17 86 82 49 43 3 7 61 79 19 16 56 87 96 41 88 83 2 8 36 00 91 93 65 15 41 23 96 38 3 7 85 45 34 68 16 73 45 54 19 79 2 8

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 4 4

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 _____. This scenario seems very unlikely, so our gentleman does have a case for discrimination. 0%

Assignment: Outline and Conduct a Simulation for Each p. 398 #4 (Line 125) Run 5 trials; 0 to 6  shot made 7 to 9  shot missed p. 402 #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!