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Emily DeAngelis Megan Wolf

Emily DeAngelis Megan Wolf. AP Stat Final Project. 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

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Emily DeAngelis Megan Wolf

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  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. Test One: 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. 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

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

  10. Kitchen Suspects

  11. Ballroom Suspects

  12. Conservatory Suspects

  13. Dining Room Suspects

  14. Billiard Room Suspects

  15. Library Suspects

  16. Lounge Suspects

  17. Hall Suspects

  18. Study Suspects

  19. Test One Calculations: Chi-Square Test of Association p( > 52.9739) = 0.082145 =S(obs-exp)2= (7-6.2857)2+ (5-5.7619)2+ . . . exp 6.2857 5.7619 = 52.9739 df(# of rows-1) x (# of columns-1) = 40 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.

  20. Bar Graph Occurrences Conservatory Kitchen Ballroom Dining Room Billiard Room Library Lounge Hall Study Room

  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. 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. 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

  23. Suspects

  24. Mustard’s Weapon

  25. Green’s Weapon

  26. Scarlet’s Weapon

  27. Peacock’s Weapon

  28. Plum’s Weapon

  29. White’s Weapon

  30. Test Two Calculations: Chi-Square Test of Association =S(obs-exp)2= (9-8.1778)2+ (7-9.0667)2+ . . . exp 8.1778 9.0667 = 31.7066 df(# of rows-1) x (# of columns-1) = 40 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.

  31. Bar Graph Occurrences Revolver Rope Dagger Lead Pipe Candlestick Poison Wrench Weapon

  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

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