## Inferential Statistics Retake Test

### 5 points each for a maximum of 60 points, hence you can only achieve 60 of the 100 points which were possible on the inclass test

Questions are based on the roster you downloaded for the first retake test, if you did not take that test, you will need to download a roster.
1. Construct a 95% confidence interval for the mean weight of football players assuming your team is a random sample.
2. How large a sample would you need (assuming the standard deviation from your team is the population standard deviation) to have a 95% confidence interval with a 5 pound margin of error.
3. If one used the weights of all the football players in the conference rather than just one team, how would that change the resultant confidence interval?
4. Construct a 99% confidence interval for the percentage of players who are backfield.
5. Give two changes in a confidence interval that would indicate that the sample mean is a more accurate estimate of the population mean.
6. Perform a test of hypothesis of whether half the players are offense, using your team as a sample; whether more than half the players are offense, whether fewer than half the players are offense.
7. Discuss what it would mean (interms of tests of hyupotheses) if the mean weight of the UNI football team was/was not in the 95% confidence interval which you constructed from the weights of your team.
8. If you wanted to demonstrate that professional football players are heavier than college football players, what would your null and alternative hypotheses be?
9. For the null and alternative hypotheses in 8 above, what would a type I error be, and how would it occur? What would a type II error be, and how would it occur?
10. Perform a goodness of fit test for the hypothesis that there are an equal number of defense and offense players. Compare the result to your answer in 6 above.
11. Do a goodness of fit test to check whether the number of players on the roster for specified positions is proportional to the number who play in a game (are on the field at one time) (in order to have large enough cell sizes, you might want to use the four categories offensive line, offensive backfield, defensive line, defensive backfield).
12. Do a test of independence of whether offense versus defense is independent of instate versus out of state [or line versus backfield is independent of big 10 versus other conferences, or division I versus other divisions; use any two way partition for which sample sizes will be large enough].
December 2014