Advanced Placement Statistics Section 6 1 Simulation EQ

Terms to Know: • Simulation --- model that imitates chance behavior of some

• probability of outcomes multiple of 10% use 0 to 9 • other

• Trial or Repetition --- repeated simulations • Independence --- the outcome of

Outline for a Simulation: Step 1: State problem Step 2: State assumptions State

Step 4: Conduct a trial Simulate repetitions Record results Summarize data State your conclusions.

Problem: What is the likelihood that all 10 randomly selected students at a particular

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

Model: • Use a random digit table to simulate selecting 10 random students from

Conduct Trial/Record Results: Use Line 129 on Table B. Write the digits on your

Conclusions: Based on this simulation, we can conclude if 10 students from this university

Ex. 2: Is This Discrimination? p. 399 • Set up and run a

State Problem: What is the likelihood that at least 6 out of 10 randomly

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

Model: • Use a random digit table to simulate randomly selecting 10 fired employees

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

RESULTS: Random Digits TRIAL 1 95 59 29 40 07 69 97 19 14

Number of Salespeople 55 or Older Frequency of Trials with this Outcome 0 0

Conclusion: Based on our simulation, the probability that 6 or more sales people in

Assignment: Outline and Conduct a Simulation for Each p. 398 p. 402 #4 (Line

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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 ØDO 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.

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 Tues Thurs Mon Fri

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

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

Number of Salespeople 55 or Older Frequency of Trials with this Outcome 0 0 1 2 3 4 5 6 7 8 9 10 2 4 4 0 0 0 0

Conclusion: Based on our simulation, the probability that 6 or more sales people in a randomly selected group of 10 fired sales people 0% are 55 years old or older is _____. This scenario seems very unlikely, so our gentleman does have a case for discrimination.

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