1. “Not the real deal but close” Ch 11 Simulations

2. Real World Example https://www.youtube.com/watch?v=IcS2VUoe12M This is a simulation of what it feels like to experience autism related sensory overload in a fairly typical life experience. Time 2:39

3. Vocabulary Simulation – process that (artificially) replicates[models] a real life scenario through a sequence of random outcomes Trial/Event – one sequence that mimics all aspects [components] of the problem Response variable…recorded outcome of each trial

4. Key parts of the process All aspects [components] of the original problem should be matched by the simulation All steps must be explained – showing that connection [i.e. describe/explain what a full trial is for your scenario] Trials must be repeated (approx 20 “by hand”; 1000’s with computer simulations) with results organized/shown in a table Conclude your simulation with a written summary of your conclusions. Show your math!!!

5. TOOLS Technology Graphing calculator’s random integer generator Computer programs such as www.probexplorer. com www.probexplorer. com Low-tech Random Number Table Dice Deck of cards Limited only by your imagination

6. Examples: Note #1: On the next several slides you will see a 5 step process on the left with an example from your text worked out on the right [#14]. Be sure to copy the steps…they represent the steps in the process I need to see on the page for you to receive full credit on quizzes or tests. Note #2: Most simulations will either be “discrete” like the one we are about to see or “open ended” like problem #22 in your text which we will do together in class for notes.

7. STEPS and EXAMPLE #14 ch 11 NOTES: 1. Identify the components/event to be replicated (can be written out – I encourage you to write this out especially with hw/practice-try framing the situation as an “essential question” first…many students have found that step really helpful) EXAMPLE: Essential question: “How likely is it that my friend randomly guessed their way to a perfect quiz?” 6 quiz questions Multiple choice with 4 possible answers (a,b,c,d) Friend guessed blindly (random guessing) so 25% chance of being right and 75% of being wrong

8. Continued: step 2 Identify your tool and Explain (in detail) how you will model each trial using the tool of your choice. Define the variable you will be “counting” after each trial and recording in your table. Typically in AP Stat we use random number table or GC…I will demo the random number table now and the gc for ex #2 Note the first two bullet points must be written out as part of your solution for credit to be fully earned!! (tool: Rand Num Table) Proces = Select a row and go through digits until you have 6 quiz “answers” where 1 = right answer; 2-4 = wrong answers; ignore/skip 0 & 5-9. Do not worry about repeats since numbers represent percentages. With the Rand Num Table you must always adress #’s out of range With all tools you must adress issue of “repeats” Variable = Count # of “correct answers”

9. Continued: step 3 Repeat your trial several times. [the problem usually tells you how many trials to run]. Organize your trials in a table – you might want to set this up in step 2…it will help you define your variable Each trial = one quiz taken via random guessing…variable = # correct TRIAL# correct 4,4,1,3,2,31 correct 1,2,4,1,4,42 1,2,1,4,1,14

10. Continued: step 4 Analyze your results…how you do this depends on the question….should you make a graph of the results and analyze like Unit I?….calculate an average of your results?…describe it in a sentence?….etc. Must show and explain math in this step for full credit”!!! For this problem I might (option 1-most common) Calculate the “average” number of correct answers…it is really critical to show your denominator!! (option 2-alternative idea) show a dot plot for the number correct and use graph to argue my answer to the next step visually

11. Final Step – step 5 Explain the results you have found. Clearly state your conclusion based on your simulation. Start with the phrase… “Based on my simulation, ….” Based on my simulation of ___randomly guessed multiple choice quizzes, I highly doubt my friend was able to just blindly guess 6 correct answers in a row since in __ simulations the average number right was ____ and I never had a perfect “quiz” result.