A common activity in physical education classes is the running “beep test,” where students must run a certain distance across a gym, then wait for a beep to run back. This process continues back-and-forth across the gym until the student fails to reach the other side before the beep and must stop. Each time the student successfully beats the beep is called a “rep.” A student in a large high school recruited 50 other students to participate in an experiment to determine if playing motivational music during the beep test would improve performance. The students were randomly assigned to two groups: one group completed the beep test with motivational music playing in the background; the other group completed the beep test without anything being played. The groups completed the test at separate times without seeing the other group compete. The back-to-back stemplot below summarizes the results of the beep test for the two groups.
One student who participated in the experiment will be selected at random.
(a) What is the probability that the selected student completed fewer than 100 reps?
(b) What is the probability that the selected student completed fewer than 100 reps, given that they ran without music?
Write a few sentences comparing the distribution of reps completed for the two treatments.
An appropriate statistical test concluded that there was a statistically significant difference between the treatments. Explain what “statistically significant” means in this context.
In the context of this scenario, explain why randomly assigning the participants to their groups was important.