Stats 8/26/13 1. Check homework C11 #2-9 Ch 11 Practice To do (assignment): C11 #10-19 for Tuesday – be ready to turn in all C11. Read/Notes for C12 by Thursday

Ch 11 Reading Quiz – Open Note List the 7 steps for doing a simulation, in order.

C11 #2-9 2. Probably random or pseudorandom with each outcome 00,0, 01-36 equally likely. 3. It is random if each ball is generated in an unpredictable and equally likely fashion. 4. Rolling a die – 6 equally likely outcomes. Rolling two dice – 36 equally likely outcomes Spinner – each should be equally likely but depends on design Dealing cards – equally likely if well shuffled only 5. a. The outcomes are not equally likely – P (5/9 heads) is not the same as P (0 heads) etc. b. Assignment assumes a player is equally likely to miss/hit, which is probably not the case. C. This does not take into account that the likelihood of getting an ace, for example, changes as cards are drawn and not replaced. 6. a. Sums are not equally likely – there are 6/36 ways to get a 7, but only 1 way to get a 2. b. The probability of having 1 boy is not the same as having 3 boys, etc. C. The probabilities of out, single, double, etc. are not really equal. 7. The average length should be around 3.2 people, but any particular trial will not get exactly 3.2 people. 8. 24% of people may contact disease on average, but real result may not be exactly 24%. 9. we’ll go over

Generating Pseudorandoms Seeding calculator MATH -> PRB You are welcome to use calculator for homework. Quizzes/tests will require use of tables. You have to know how to use both well.

Simulating Random Processes – Method 1 for Generating Data to Answer Statistical Questions 1. Identify simulation as appropriate method. 2. Identify repeating event/component in simulation. 3. Explain how you will use random digits to represent/model the outcome each time. 4. Explain how you will simulate/pretend through a complete trial – including how you will generate the digits, decide what they mean, and when you will stop.

Simulation steps continued 5. State clearly what the result of your trial is. 6. Repeat for several trials (5 for homework, as many as possible in reality, as many as asked on quizzes/tests). 7. Analyze your trial results (usually this means computing an average). 8. Give an answer/conclusion to the question you were trying to answer by simulation, IN CONTEXT.

Example - #13 page 224 You are about to take the road test for your driver’s license. You hear that only 34% of candidates pass the test the first time, but the percentage rises to 72% on retests. Estimate the average number of tests drivers take in order to get a license. Your simulation should use at least 20 trials/runs.

The steps – must always do ALL for simulations 1. given 2. We will simulate 20 people taking the driver’s test until they pass. 3. 34% pass the first time, and 72% pass on retries. So on a first try, I can read two-digits numbers from a random number table and let 00-33 represent passing, 34-99 failing. On retries, 00-71 can represent passing, 72-99 failing. (On a calculator, I could use randInt(1,100) and use 1-34 to represent passing first, and 1-72 to represent passing retries).

Example #13 continued 4. A complete trial will look like this: I will use the method described in #3 to generate the first two digit number. If it represents passing the test, I will stop, and record that it took 1 try to pass. If it does not represent passing, I will generate a second two-digit number. If it represents passing a retry, then I will stop and record that it took 2 tries to pass. If not, I will repeat as many times as necessary until a pass is achieved and record how many tries it took. That will be one trial.

Example #13 continued Steps 5 – 8 (let’s do it and see what we get!)

Watch Out Make you’re your modeling assigns random digits to events in such a way that the proportion of digits assigned to an outcome EXACTLY matches its probability. You may need to use two digit numbers and not just one digit numbers. Random number table – if you’re using double digits, the biggest number you can get is 99 – that’s an issue when working with percents – be careful!