Football and Brain Size A recent study examined the relationship of football and concussions on hippocampus volume in the brain. The study included three groups with $n=25$ in each group: heathy controls who had never played football, football players with no history of concussions, and football players with a history of concussions. Figure 2.41 shows side-by-side boxplots for total hippocampus volume, in $\mu \mathrm{L}$, for the three groups.

(a) Is the explanatory variable categorical or quantitative? Is the response variable categorical or quantitative?

(b) Which group has the largest hippocampal volume? Which group has the smallest?

(c) Are there any outliers in any of the groups? If so, which one(s)?

(d) Estimate the third quartile for the football players without a history of concussion.

Figure 2.41 Relationship of football and concussions on brain hippocampus size

(e) Does there appear to be an association between football experience and hippocampus size?

(f) Can we conclude that playing football decreases hippocampus volume? Why or why not?

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Total Hippocampus Volume 10000 9000 8000 7000 6000 5000 4000 Control Football No Concussion Football With Concussion Group