Question

Ms.Watts is a fan of college football, and is a little bummed the Texas Longhorns haven’t been doing as well these past few years. She has a hunch that because The Longhorns are in the highest collegiate athletic division (Division-I), her team is more likely to play a mismatched opponent. That is, The Longhorns are more likely to play games with different point spreads (winning team’s score minus losing team’s score) compared to other Divisions. To test this idea, she looked at a sample of 4 games from a lower division (Division-II) to see if the mean point spread was different compared to The Longhorns’ Division-I group. Overall, Division-I teams had a mean spread of 16.189 points with a standard deviation of 12.128 points.

1. The results of the four Division-II games from Ms. Watt's sample are below. Calculate the mean point spread for this sample.

Team 1 / SCORE	Team 2 / SCORE	Point Spread (T1 Score - T2 Score)
Holy Cross / 27	Bucknell / 10
Lehigh / 23	Colgate / 15
Lafayette / 31	Fordham / 24
Georgetown / 24	Marist / 21
	MEAN

2. Calculate the standard error.

3. State the null hypothesis based on what Ms.Watts believes about mean point spreads in Division-I compared to Division-II football games.

4. State the research hypothesis based on what Ms.Watts believes about mean point spreads in Division-I compared to Division-II football games.

5. Calculate the z-statistic to test the hypothesis you formulated in Questions 3 & 4 using the mean point spread for Division I as the comparison population to the mean point spread you calculated for #1.

6. Given the convention of p<.05, what can you conclude about the mean point spread found in Division-II compared to the mean point spread in Division-I teams? First, make a decision regarding your hypothesis, then state your conclusion.

Answer 1

1.

Team 1 / SCORE	Team 2 / SCORE	Point Spread (T1 Score - T2 Score)
Holy Cross / 27	Bucknell / 10	17
Lehigh / 23	Colgate / 15	8
Lafayette / 31	Fordham / 24	7
Georgetown / 24	Marist / 21	3
	MEAN= (17 + 8 + 7 + 3) / 4 = 8.75

mean point spread for this sample = 8.75

2.

Standard deviation of point spread = sqrt{[(17 - 8.75)² + (8 - 8.75)² + (7 - 8.75)² + (3 - 8.75)² ] / 3}

= 5.909033

Standard error of mean difference between mean point spreads in Division-I compared to Division-II football games is,

= 6.745455

3.

Null hypothesis H0: Mean point spreads in Division-I is equal to mean point spreads in Division-II football games. That is

4.

Research hypothesis H0: Mean point spreads in Division-I is greater than the mean point spreads in Division-II football games. That is

5.

z-statistic = Differences in Mean point differences / Standard error

= (16.189 - 8.75) / 6.745455

= 1.10

6.

P-value = P(z > 1.10) = 0.1357

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that true mean point spreads in Division-I is greater than the true mean point spreads in Division-II football games.