Exercise 2.143 introduces a study examining the relationship between football playing and hippocampal volume, in \(\mu \mathrm{L}\), in the brain. We use the \(n=25\) participants in the control group to estimate average brain hippocampus volume for all non-football playing people. Use the dotplots in Figure 3.20 to answer the following questions.

(a) Two dotplots are shown: one shows the original data and one shows a bootstrap distribution from the data. Which is which?

(b) Estimate the sample mean hippocampal volume based on the graphs. Give the correct notation and the value.

(c) Use the graphs to roughly estimate the standard error if we use this sample mean to estimate hippocampal volume.

(d) Does the standard deviation of the original data appear to be larger or smaller than the standard error?

(e) Use the estimated mean and the estimated standard error to find and interpret a rough \(95 \%\) confidence interval for the mean hippocampal volume.

Data From Exercise 2.143:

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.

Figure 2.41:

Transcribed Image Text:

00 6000 6500 7000 7500 8000 8500 9000 9500 10000 Dotplot I Figure 3.20 Which is the bootstrap distribution? 7000 7200 7400 7600 7800 8000 8200 Dotplot II