Researchers have often noted increases in violent crimes when it is very hot. In

Question

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 aseball. 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 s = 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.

Explanation / Answer

The test hypothesis is
Ho: <=12
Ha:>12

The test statistic is

t=(xbar-)/(s/n)

=(15.5-12)/(3/2)

=2.33

Given a=0.05, the critical value is |t(0.05, df=n-1=3)|=2.35 (check student t table)

Since t=2.33<2.35, we do not reject Ho. So we can not conclude that players are more likely to get hit by pitches during hot weeks

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