Using data from Exercise 13.25, we used a randomization test to find out whether the typical number of winning runs in the American League differed from that of the National League in professional baseball. In each randomization we found the mean difference between the two groups that were randomly selected from the combined group of data: the combined data for the American and National Leagues. Note that, just as you would expect under the null hypothesis, the distribution is centered at about 0. The observed difference in means (American League - National League) was 0.1086 and is shown by the red vertical line. Use the output provided and a significance level of 0.05 to determine if typical number of winning runs differs between the two leagues. How does this answer compare with your conclusion when using the Mann-Whitney test in exercise 13.25?

Exercise 13.25

Is there a difference in the runs scored by winning teams in the American League and the National League in professional baseball? The winning scores for all games played on two randomly selected days were recorded and the league of the winning team was noted. The histogram below shows the winning scores for teams in the National League.

Frequency 250 200 150 - 100 50 -4 -2 0 2 4 6 Randomized statistics