Both #1 and #2 will receive full credit. In #2, you do a good job of comparing the distributions instead of just describing. Your description of “bimodal” for the “without music” side is a bit weak (I’d go with “skewed left”), but given the stemplot it would likely be accepted.
In #3, your description is lacking - while this is a “proper experiment,” that doesn’t explain what “statistically significant” actually means. This is a bit of an obscure definition, but “statistically significant” is what we mean when we have a “low p-value”… so that means that the observed differences between the treatment groups are unlikely to have occurred by chance (which means that we would reject a null hypothesis that the treatment groups would have no difference). So in this case, we would need to say something like “statistically significant in this context means that the difference in the mean number of reps completed by the two groups is unlikely to have happened by random chance; we can therefore conclude that the treatment caused the difference” (or something in that ballpark)
In #4, you get partly there - your description of getting “rid of distractions” or “different skill levels” is an in-context description of reducing possible confounding variables through randomization, but your description does not explicitly connect this to the response variable in question: the number of reps completed. Any answer about a “why” in an experiment/observational study should come back to the response variable. A way to strengthen your response could be saying something like “there’s an opportunity to get different skill levels on agility and reduce distractions from friends, which will allow us to compare the number of reps completed by each group more easily and fairly.”
Overall, you’ve given strong responses. Your answers in the final three parts will need to have a little more context from the problem involved. On to the feedback:
For the probability calculations, you have gotten the correct values with appropriate work shown.
When comparing the distributions, you provide appropriate comparisons of shape, center, and spread. However, while you compare the group “with music” vs “without music,” you never mention what was being measured about the groups that you are comparing. In this case, it is the number of repetitions (reps) completed. Be sure to mention the variable in your answer; for example, “the range of number of reps completed is larger for the distribution with music than without”
While discussion “statistical significance,” you give a correct definition - the results are unlikely to have occurred by chance alone - but you do not describe what the results are in this case. That is, you should say “the difference in the mean number of reps completed by the two groups is so low that it would not have been unlikely (not impossible, as you say) to occur by chance.” Similarly, when discussing random assignment, you should give a possible reason for why students choosing their group would potentially introduce confounding to this experiment. (Perhaps they will try harder when competing against their friends, regardless of the music playing). All of your responses would likely earn partial credit, but to get full credit, you must include the context of the problem in your answers.
Nice work! All answers are correct, but some little things may prevent you from getting full credit.
In part 1 - you have to show where the 0.26 and 0.4 came from. Those are considered “naked answers” and must have the accompanying fractions shown to illustrate your work.
Then in part 2 - you list both medians, but don’t compare them with a comparison term. Yup, you have to spell it out for us readers… we’re not allowed to assume that you know 122 is larger that 101, as ridiculous as that sounds!