Warm-up What is the best way to answer each of the questions below: an experiment, a sample survey, or an observational study that is not a sample survey? Explain. –Are people generally satisfied with how things are going in the country right now? –Do college students learn basic accounting better in the classroom or using an online course? –How long do your teachers wait on average after they ask their class a question?

Section 5.1 Simulations

Simulations What are they? –Imitations of an experiment – a way to calculate the probability of something happening without actually carrying out the experiment Why do we use them? –It can be quicker and/or less expensive than actually carrying out the experiment. –The laws of probability can be confusing. Simulation makes sense.

Example Suppose I want to know the probability that a couple has a girl among their first four children. Assume that the probability of having a boy = the probability of having a girl = 0.5 What real life object simulates 2 outcomes of equal likelihood?

Example Continued So, we could designate HEADS = having a girl. Simulation: Toss the coin 4 times and record whether HEADS shows up at least once. Repeat this 10 times and compute the probability.

Instead of a coin… You could use your calculator. –ProbSim, Choose Coin Toss, you can change the set to toss 4 coins at a time. –Choose 4 random integers between 1 and 2. Let 1 = girl. MATH/PRB/5: RANDINT(1,2,4) Repeat and compute the probability. You could use the table of random digits. –Choose digits 4 at a time. Let even = girl. –Repeat and compute the probability. Let’s do this starting on line 113. Complete 10 trials.

Synopsis of the Steps in a Simulation 1)State how you will assign digits to represent outcomes. State which digits you will “throw out”. Can you have repeats? 2)State the assumptions. oEach digit is equally likely oEach digit is independent of one another 3)Tell how you will simulate and then simulate many repetitions. oTable B or Calculator? Be specific. oHow many digits will you look at one time. oWhen will you stop? 4)State your conclusions. Be sure to answer the original question.

Example Shaq’s forte is definitely not on the free throw line. Let’s assume he is a 60% free throw shooter. How could we simulate an experiment to see how many shots he would have to take to make 4 in a row? How would this problem change if Shaq is a 57% free throw shooter?

Example About 7% of men in the United States have some form of red- green color blindness. Suppose we randomly select 4 US adult males. What percent of the time would we select at least one male who is red- green color blind? –Each group should conduct 20 repetitions of this and count how many times at least one male is “color blind.”

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