Simulating Experiments on the TI Section 5.3.2

Starter Use the random integer generator in your calculator to choose an SRS of 5 students from this class of 35. –The command is randInt(1, 35) Keep going until you have 5 non-duplicated numbers –More efficient command: randInt(1, 35, 5) generates the numbers 5 at a time With luck, this will give you 5 non-duplicated numbers with only one command. If it happens that there IS one or more duplications in the sample, repeat the command until you have the desired amount on non-duplicated numbers.

Ensuring We All Agree If I want you to all get the same sample (as in a test), I would tell you which line of the random number table to use. We can do the same on the TI with the rand command. –Enter the following: 247 →rand This is called “storing a seed” to the random number generator. –Now enter randInt(1, 35, 5) –Your sample should be students #6, 15, 24, 32, 22

Objectives Estimate probability-based outcomes of studies based on properly designed simulations and the use of a calculator’s random integer generator.

Calculator-based Simulations As with table-based simulations, the major issue is the assignment of digits to outcomes. The calculator is easier because you control which digits are possible. –With two equally likely outcomes (like coin flips), just use two digits like 0&1 or 1&2. The other digits that appear on a table are not needed here. –With two or more outcomes that are not equally likely, choose ranges of one-digit or two-digit (or more) numbers that reflect the underlying probabilities of the problem.

Example: Yesterday’s Basketball Problem A basketball player normally makes 62% of her free throws. If she takes 5 free throws in tonight’s game, What is the likelihood that she makes at least 3 of them? The hard part of this question is to figure out the assignment of digits. Think it through and carry out a simulation of 3 games. Combine class results and draw a conclusion It turns out that the theoretical answer is.716

Doing a large number of repetitions We have just seen that a single calculator command that generates multiple outcomes is a much faster way to do a simulation. That makes it practical for one person to do enough repetitions to get reasonable estimates of likelihood in a short time. Re-do the basketball problem with a normal free- throw percentage of 81% and 20 repetitions. Write your conclusion based on the 20 trials you just did. The theoretical value is.949

Using a program for simulations Link calculators to get the FREETHRO program. The program generates 100 equally likely outcomes, considers 62% of them to be “successes”, and displays the relative frequency of success Run the program to re-do the 62% basketball problem with 50 trials. Modify the program and re-do the 81% problem with 100 trials.

Objectives Estimate probability-based outcomes of studies based on properly designed simulations and the use of a calculator’s random integer generator.

Homework Read pages 293 – 295 Do problems 58, 59