1. Emily DeAngelis Megan Wolf AP Stat Final Project

2. History of Clue ® Originally published in Britain during the late 1940s under the name Cluedo Developed by a young British law clerk named Anthony Pratt Pratt would play a game called Murder at friends’ dinner parties similar to the idea of Clue Took many years to finally perfect the game partially due to delays during World War II

3. Directions for Clue Game takes place in the mansion of Mr. Boddy who has been murdered One of the six guests in the house committed the murder Goal is to solve the murder case by finding the suspect, murder weapon, and room the crime took place A suspect, weapon, and room card are selected at random and it’s the players job to solve the case

4. Rooms

5. Weapons

6. Suspects

7. Collecting Data Split cards into piles labeled suspects, room, and weapon Picked card from each pile and wrote down results Replaced card and shuffled deck Repeat

8. Hypothesis: Ho: There is no association between picking suspect and room cards. Ha: There is an association between picking suspect and room cards. Assumptions: State: 2 independent SRS Sample size large enough that all expected values are greater than or equal to 5 Check: Assumed Refer to chart Test One: Chi-Square Test for Association

9. Game Board Dining Room Kitchen Billiard Room Conservatory Hall Lounge Study Ballroom Library

10. ExpectedObserved 62 5.44444 5.77789 Kitchen Suspects ExpectedObserved 6.33337 6.11117 5.33336

11. ExpectedObserved 5.82861 5.28896 5.61277 Ballroom Suspects ExpectedObserved 6.15247 5.93655 5.18108

12. ExpectedObserved 5.657111 5.13337 5.44765 Conservatory Suspects ExpectedObserved 5.97144 5.76191 5.02865

13. ExpectedObserved 6.17146 5.65 5.94295 Dining Room Suspects ExpectedObserved 6.51438 6.28577 5.48575

14. ExpectedObserved 5.82866 5.28897 5.61279 Billiard Room Suspects ExpectedObserved 6.15243 5.93657 5.1812

15. ExpectedObserved 6.685713 6.06675 6.43811 Library Suspects ExpectedObserved 7.05719 6.80955 5.94296

16. ExpectedObserved 5.82863 5.28894 5. 61274 Lounge Suspects ExpectedObserved 6.15248 5.936510 5.18105

17. ExpectedObserved 6.34299 5.75564 6.10797 Hall Suspects ExpectedObserved 6.69523 6.46038 5.63816

18. ExpectedObserved 5.65713 5.13337 5.44765 Study Suspects ExpectedObserved 5.97148 5.76195 5.02865

19.   obs-exp) 2 = exp (7-6.2857) 2 + (5-5.7619) 2 +... 6.2857 5.7619 = 52.9739 p(> 52.9739) = 0.082145 Conclusion: We fail to reject Ho because our P-value is greater than alpha (0.05). We have sufficient evidence that there is no association between picking suspect and room cards. df (# of rows-1) x (# of columns-1) = 40 Test One Calculations: Chi- Square Test of Association

20. Bar Graph KitchenLibraryLoungeHallStudyDining RoomBilliard Room Conservatory Ballroom Room Occurrences

21. Analysis/ Conclusion of Bar Graph It appears as though the bar graphs for the dining room, hall, and study are normally distributed with the dining room being almost uniform For the other graphs however there are possible outliers because of the varying heights of the bars Some graphs appear unimodal because the highest peak involves one suspect All have good spreads

22. Assumptions: State: 2 independent SRS Sample size large enough that all expected values are greater than or equal to 5 Check: Assumed Refer to chart Test Two: Chi-Square Test for Association Hypothesis: Ho: There is no association between picking suspect and room cards. Ha: There is an association between picking suspect and room cards.

23. Suspects

24. Mustard’s Weapon ExpectedObserved 8.17789 9.06677 87 8.35566 ExpectedObserved 87 7.288915 7.11115

25. Green’s Weapon ExpectedObserved 8.17789 9.06677 86 8.355613 ExpectedObserved 87 7.28896 7.11118

26. Scarlet’s Weapon ExpectedObserved 7.59379 8.4198 7.42869 7.75877 ExpectedObserved 7.42866 6.76837 6.60326

27. Peacock’s Weapon ExpectedObserved 7.44767 8.257110 7.28579 7.609510 ExpectedObserved 7.28573 6.63815 6.47627

28. Plum’s Weapon ExpectedObserved 6.86357 7.60956 6.71437 7.01275 ExpectedObserved 6.714312 6.11754 5.96836

29. White’s Weapon ExpectedObserved 7.73975 8.58113 7.57147 7.90796 ExpectedObserved 7.571410 6.89844 6.73028

30.   obs-exp) 2 = exp (9-8.1778) 2 + (7-9.0667) 2 +... 8.1778 9.0667 = 31.7066 p(> 31.7066) = 0.38140 Conclusion: We fail to reject Ho in favor of Ha because our P-value is greater than alpha (0.05). We have sufficient evidence that there is no association between picking suspect and weapon cards. Test Two Calculations: Chi- Square Test of Association df (# of rows-1) x (# of columns-1) = 40

31. Bar Graph Revolver PoisonWrenchLead PipeCandlestickDaggerRope Weapon Occurrences

32. Analysis/ Conclusion of Bar Graph The bar graphs for the revolver, dagger, and wrench look normally distributed with the dagger being almost uniform, while the other 2 are a little skewed. Meanwhile in the bar graphs for the rope, lead pipe, candlestick, and poison there appear to be outliers because it is not normally distributed and some bars are much longer than others. Some graphs appear unimodal because the highest peak involves one suspect All have good spreads

33. Bias/Error Our experiment was conducted through random samplings of the 22 cards (no bias) An example of a bias experiment would be if we had arranged or drawn the cards in a specific order or pattern as to predict/control the outcomes which we did not do If the 315 samples would be collected by different people, every person would have to collect data under the same conditions Possible error for our experiment was that the cards weren’t shuffled enough in between each sample

34. Personal Opinions/Conclusions We believe that our outcomes match the expected values Therefore the game is completely fair The suspect, room, and weapon used is chosen randomly because there is no extra advantage

35. Application For everyone who plays the board game Clue, it is a fair game and not one person has an extra advantage.

36. Class Activity Answer statistics review questions If correct you are given a clue as to who committed the murder, where it was at, and with what was used When the class figures out the suspect, weapon, and room, you win a prize