The football coach at State University wishes to determine if there is a decrease in offensive production between the first half and the second half of his team's recent games. The table below Shows the first-half and second-half offensive production (measured in total yards gained per half)
For the past six games. Compute the test statistic.
A) 9.895
B) 2.881
C) 1.288
D) 3.165

Question

The football coach at State University wishes to determine if there is a decrease in offensive production between the first half and the second half of his team's recent games. The table below Shows the first-half and second-half offensive production (measured in total yards gained per half)
For the past six games.  Compute the test statistic.
A) 9.895 
B) 2.881 
C) 1.288 
D) 3.165

Quizplus · Accepted Answer

To compute the test statistic, we can use a paired samples t-test since we are comparing the same group of players in two different halves of the same game. Using a calculator or software, we can find the mean difference between first-half and second-half production to be -18.33 yards with a standard deviation of 16.32 yards. We can then compute the t-statistic as: 
t = (mean difference - hypothesized difference) / (standard deviation of the differences / sqrt(number of pairs))
Since we want to test if there is a decrease in production, our hypothesized difference is 0. We have 6 pairs of data (6 games), so 
t = (-18.33 - 0) / (16.32 / sqrt(6)) = -3.165
Rounding to 3 decimal places, we get a test statistic of  -3.165, which is closest to answer choice D.

The Football Coach at State University Wishes to Determine If