In problem #4 of homework #5, we have the velocity of fastballs thrown by 10 college baseball pitchers. This is data taken in 2012, and the observations are below.

81.9 77.7 80.3 83.1 89.5 85.4 87.9 88.9 78.1 84.9

Suppose in 1992, the same variable was measured on a sample of 7 college pitchers. The observations are below.

75.6 77.3 82.1 74.1 81.8 76.6 80.3

We want to test, at = .10, if there is a difference in the median velocity for the two years.

Calculate the test statistic of the Wilcoxon rank sum test, "by hand". You do not have to compare this to a rejection region, and you do not have to interpret the result (yet). (4 pts)

Use PROC NPAR1WAY (with the EXACT subcommand) to calculate the test statistic. Turn in the printout, state the best p-value to use for the test, and now interpret the result. (6 pts)

data six;

input year n @@;

do i = 1 to n;

input velocity @@;

output;

end;

drop i n;

datalines;

2012 10 81.9 77.7 80.3 83.1 89.5 85.4 87.9 88.9 78.1 84.9

1992 7 75.6 77.3 82.1 74.1 81.8 76.6 80.3

;

run;