Ms.Watts is a fan of college football, and is a little bummedthe Texas Longhorns haven’t been doing as well these past fewyears. She has a hunch that because The Longhorns are in thehighest collegiate athletic division (Division-I), her team is morelikely to play a mismatched opponent. That is, The Longhorns aremore likely to play games with different point spreads (winningteam’s score minus losing team’s score) compared to otherDivisions. To test this idea, she looked at a sample of 4 gamesfrom a lower division (Division-II) to see if the mean point spreadwas different compared to The Longhorns’ Division-I group.Overall, Division-I teams had a mean spread of 16.189points with a standard deviation of 12.128 points.
1. The results of the four Division-II games from Ms. Watt'ssample are below. Calculate the mean point spread for thissample.
| 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 whatMs.Watts believes about mean point spreads in Division-I comparedto Division-II football games.
4. State the research hypothesis based on whatMs.Watts believes about mean point spreads in Division-I comparedto Division-II football games.
5. Calculate the z-statistic to test the hypothesis youformulated in Questions 3 & 4 using the mean point spread forDivision I as the comparison population to the mean point spreadyou calculated for #1.
6. Given the convention of p<.05, what can youconclude about the mean point spread found in Division-II comparedto the mean point spread in Division-I teams? First, make adecision regarding your hypothesis, then state your conclusion.
