In the previous class, students gathered data from their simulations and used it to complete the results table found in Basketball Experiment Tables. Today, students put their results together with those of their classmates.
Once students are settled, I begin to make a large dot-plot on the board. I ask students for help in determining what numbers to put on the horizontal axis (-100 to 100). I ask a member of each of yesterday's pairs to take their results table to the board and accurately plot their group's five data points.
When all 100+ dots are on the plot, I ask students to recall what each dot represents. I hope they will be able to articulate that each dot represents a possible difference in percent of shots made if the distraction played no part in whether the shot was made or not. Students take a few moments to make a sketch of this dotplot on Basketball Experiment Part 1 [MP4].
I remind students that in the actual experiment, the difference was 50%. Citing our results as evidence, I ask students to discuss whether or not the distraction affected the number of shots that went in. They then answer the final questions on Basketball Experiment Part 1 and turn this in to me.
I hope that the hands-on simulation we just completed will give my students a concrete understanding of randomization as a method of assessing significance. I also want them to know that many more trials of the randomization make the conclusions more robust. Because doing thousands of trials by hand is not practical, we turn to computer-based simulations.
Students work with the same partner as they did the previous day to complete Basketball Experiment Part 2. Each pair of students needs access to a laptop to complete this activity. To scramble the results thousands of times, we use a free applet. Each pair of students generates 6000 randomization trials and then uses the results to assess the probability of getting a difference in proportions as large as 50% by chance alone [MP3, MP4].
As a class, we conclude the simulation activity by discussing our results. Each pair of students performed the computer simulation separately, so their probabilities will differ somewhat. I ask students to write their probabilities (p-values) on the board so we can compare.
For homework, I assign 3 simulation problems from the textbook we use for Introductory Statistics. A sample is included below.
A bag contains 10 equally-sized tags numbered 0 to 9. You reach in and, without looking, pick 3 tags without replacement. We want to use simulation to estimate the probability that the sum of the 3 numbers is at least 18. Describe the simulation procedure below, then use the random number table on the next page to carry out 10 trials of you simulation and estimate the probability. Mark on or above each line of the table so that someone can clearly follow your method.