Chapter 11, Problem 35SE

Reaction Times for Athletes A random sample of people were asked whether they were athletic, moderately athletic (Mod), or not athletic (NotAth). Then they were tested for reaction speed. Reaction speed was measured indirectly, through reaction distance, as follows: A vertical meter stick was dropped, and they caught it. The distance (in centimeters) that the stick fell is the reaction distance, and shorter distances correspond to faster reaction times. The data are shown in the following table.

a. Interpret the boxplots given. Compare the medians, interquartile ranges, and shapes, and mention any potential outliers.

b. Test the hypothesis that people with different levels of athletic ability (self-described) have different mean reaction distances, reporting the $F$ -statistic, $p$ -value, and conclusion. Assume that the distribution of each population is close enough to Normal to satisfy the Normal condition of an ANOVA and that the sample is randomly selected. Do not do post hoc tests.