If you want people to agree with you, get them to join you in a line dance or to march in lock-step with you. A recent study shows that we feel more emotionally connected to one another when we’re moving in sync. In the study, researchers asked 70 college students to walk behind an accomplice either matching stride for stride, walking completely out of sync, or walking at any comfortable pace. The students were randomly divided between the three options. After following the accomplice around campus, the students were asked to rate how close they felt to the accomplice, how much they liked the accomplice, and how similar they felt to the accomplice. Ratings were on a 7-point scale (which we will treat as quantitative) with 7 representing highest levels of closeness, liking, and similarity. On all three questions, those who had been forced to walk in sync gave substantially higher ratings than either of the other two groups.

(a) What are the cases? What is the sample size?

(b) What are the variables?

(c) Is this an experiment or an observational study?

(d) Use the information given to draw a rough sketch of possible side-by-side boxplots comparing the three groups on the similarity rankings. Be sure the sketch shows the association described.

(e) In a second part of the experiment, the students were encouraged by the accomplice to funnel live pill bugs into a grinder labeled an ‘‘extermination machine.’’ Those who had marched in step with the accomplice followed orders and ‘‘killed’’ the most pill bugs. (The pill bugs were actually secretly funneled to safety.) What graph would we use to look at a relationship of number of pill bugs killed by which treatment group the student was in? What graph would we use to look at the association of number of pill bugs killed with the rating given on the liking accomplice scale?