Example #1: The Caffeine Experiment

Does caffeine increase pulse rates? A statistics class with 20 students designed an experiment to find out. Half of the students were randomly assigned to drink cola with caffeine and the other half were assigned to drink caffeine-free cola. None of the students knew which type of cola they were drinking. Before the students consumed their beverage, they measured their initial pulse rates. Then, 10 minutes after finishing their beverage, they measured their pulse rates again, with each calculating the change in pulse rate (after – before).

What is the purpose of the random assignment? Why is this important in an experiment?

Here are the changes, along with a graph comparing the changes for the two groups:

Caffeine / 14 / 3 / –1 / 0 / 2 / 3 / 4 / –1 / 2 / 0 / Mean change = 2.6
Non-caffeine / 6 / –1 / 0 / 2 / 1 / –2 / –3 / 4 / 1 / 2 / Mean change = 1.0


Do we have evidence that caffeine increases pulse rates? Explain.

Identify two plausible explanations for why there was a higher average increase in the caffeine group.

Assuming that caffeine has no effect on pulse rates, what differences in means can we expect to occur simply due to random chance?

Example #2: The Free-Throw Experiment

Is it harder to shoot free-throws with distractions? To investigate, a basketball player went to the gym and shot 20 free-throws. Ten of the free-throws were shot without any distractions and the other 10 were shot with his friends trying everything they could to distract him. The order of the 20 shots was determined at random.

Why was it important that the order of the shots was determined at random, rather than doing all of one type of shot before the other type of shot?

The player made 8/10 (80%) of his shots in the distraction-free environment and only 3/10 (30%) of his shots in the environment with distractions, for a difference of 80% – 30% = 50%. Identify two plausible explanations for why the shooter performed better in the distraction-free environment.

Assuming that distractions have no effect on free-throw shooting, what differences in percentages can we expect to occur simply due to random chance?

Here are the results of 100 trials of this simulation. Based on these results, do we have convincing evidence that it is harder to shoot free-throws with distractions?

Simulated Difference in Shooting Percentage (no distraction – distraction)

Example #4: The Seating Chart Experiment

Many people believe that students learn better if they sit closer to the front of the classroom. Does sitting closer cause higher achievement, or do better students simply choose to sit in the front? To investigate, an AP Statistics teacher randomly assigned students to seat locations in his classroom for a particular chapter and recorded the test score for each student at the end of the chapter. The explanatory variable in this experiment is which row the student was assigned (Row 1 is closest to the front and Row 7 is the farthest away). The results of the experiment are shown below.

Why was it important to randomly assign the seats?

Does sitting close appear to help test scores? What evidence do we have?

What are the two explanations for the evidence we have?

Assuming that seat location doesn’t matter, how can we determine what slopes could arise simply by chance?

Here are the results of 100 trials of this simulation. Based on these results, do we have convincing evidence that sitting closer helps test scores?

Simulated Slope

Note: Examples from Statistical Reasoning in Sports, by Josh Tabor and Christine Franklin and the Annotated Teacher’s Edition by Josh Tabor for The Practice of Statistics 4e, by Starnes, Yates, and Moore, both published by W.H. Freeman.