My AP Statistics students complete a project on statistical inference at the end of the school year. My goal is to also conduct a project myself each year in order to model proper techniques for my students. This year, my project was on the popularity of The Avengers.

1. Avengers Assembled
BY: Mr. Yip
2012

2. 93%
(2012)

3. Captain
America
(Steve Rogers)

4. 79%
(2011)

5. Thor
(God of Thunder)

6. 77%
(2011)

7. Hawkeye
(Clint Barton)

8. Ironman
(Tony Stark)

9. 94%
(2008)

10. 74%
(2010)

11. Black
Widow
(Natasha Romanoff)

12. Hulk
(Bruce Banner)

13. 66%
(2008)

14. The Hypotheses # 1
H0: Students have no preference for an avenger.
Ha: Students have a preference for an avenger.

15. The Survey

16. Conditions for Chi-Square
Random
Large Sample Size
Independent

17. Male students n = 59
Observed
15 6 13 5 4 16
Expected
9.83 9.83 9.83 9.83 9.83 9.83

18. Results for Male Students
  14.93
2
p  value  0.011
df  5
Conclude:
Male students have a preference.

19. Female students n = 79
Observed
2 22 12 11 3 29
Expected
13.2 13.2 13.2 13.2 13.2 13.2

20. Results for Female Students
  42.76
2
p  value  0.000
df  5
Conclude:
Female students have a preference.

21. The Hypotheses # 2
H0: Avenger selection and gender are independent.
Ha: Avenger selection and gender are not independent.

22. All students n = 138
Observed
M 15 6 13 5 4 16
F 2 22 12 11 3 29

23. All students n = 138
Expected
7.27 11.97 10.69 6.84 2.99 19.24
M
9.73 16.03 14.31 9.16 4.08 25.76
F

24. All students n = 138
Observed
(Expected)
15 6 13 5 16
M (7.14) (11.76) (10.50) (6.72) (18.89)
2 22 12 11 29
F (9.86) (16.24) (14.50) (9.28) (26.11)

25. Chi-Square Test for Independence
  22.337
2
p  value  0
df  4
Conclude:
There is an association between
gender and avenger preference!

26. Potential Errors

27. Thank you !!!
Avengers Assembled
BY: Mr. Yip
2012