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Researchers have often noted increases in violent crimes when it is
very hot. In fact, Reifman, Larrick, and Fein (1991) noted that
this relationship even extends to baseball. That is, there is a
much greater chance of a batter being hit by a pitch when the
temperature increases. Consider the following hypothetical data.
Suppose that over the past 30 years, during any given week of the
major-league season, an average of µ = 12 players are hit by wild
pitches. Assume that the distribution is nearly normal with o = 3.
For a sample of n = 4 weeks in which the daily temperature was
extremely hot, the weekly average of hit-by-pitch players was M =
15.5. Are players more likely to get hit by pitches during hot
weeks? Set alpha to .05 for a one-tailed test.