Emily DeAngelis Megan Wolf AP Stat Final Project

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• 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

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

Rooms

Weapons

Suspects

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

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

Game Board

Dining Room

Kitchen

Billiard Room

Conservatory

HallLoungeStudy

Ballroom

Library

Expected Observed

6 2

5.4444 4

5.7778 9

Kitchen SuspectsExpected Observed

6.3333 7

6.1111 7

5.3333 6

Expected Observed

5.8286 1

5.2889 6

5.6127 7

Ballroom SuspectsExpected Observed

6.1524 7

5.9365 5

5.1810 8

Expected Observed

5.6571 11

5.1333 7

5.4476 5

Conservatory SuspectsExpected Observed

5.9714 4

5.7619 1

5.0286 5

Expected Observed

6.1714 6

5.6 5

5.9429 5

Dining Room SuspectsExpected Observed

6.5143 8

6.2857 7

5.4857 5

Expected Observed

5.8286 6

5.2889 7

5.6127 9

Billiard Room SuspectsExpected Observed

6.1524 3

5.9365 7

5.181 2

Expected Observed

6.6857 13

6.0667 5

6.4381 1

Library SuspectsExpected Observed

7.0571 9

6.8095 5

5.9429 6

Expected Observed

5.8286 3

5.2889 4

5. 6127 4

Lounge SuspectsExpected Observed

6.1524 8

5.9365 10

5.1810 5

Expected Observed

6.3429 9

5.7556 4

6.1079 7

Hall SuspectsExpected Observed

6.6952 3

6.4603 8

5.6381 6

Expected Observed

5.6571 3

5.1333 7

5.4476 5

Study SuspectsExpected Observed

5.9714 8

5.7619 5

5.0286 5

=S (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

Bar Graph

0

2

4

6

8

10

12

14

Mustard

Green

Scarlet

Peacock

Plum

White

Kitchen

Library

Lounge

HallStudy

Dining Room

Billiard Room

Conservatory

Ballroom

Room

Occ

urre

nces

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

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.

Suspects

Mustard’s WeaponExpected Observed

8.1778 9

9.0667 7

8 7

8.3556 6

Expected Observed

8 7

7.2889 15

7.1111 5

Green’s WeaponExpected Observed

8.1778 9

9.0667 7

8 6

8.3556 13

Expected Observed

8 7

7.2889 6

7.1111 8

Scarlet’s WeaponExpected Observed

7.5937 9

8.419 8

7.4286 9

7.7587 7

Expected Observed

7.4286 6

6.7683 7

6.6032 6

Peacock’s WeaponExpected Observed

7.4476 7

8.2571 10

7.2857 9

7.6095 10

Expected Observed

7.2857 3

6.6381 5

6.4762 7

Plum’s WeaponExpected Observed

6.8635 7

7.6095 6

6.7143 7

7.0127 5

Expected Observed

6.7143 12

6.1175 4

5.9683 6

White’s WeaponExpected Observed

7.7397 5

8.581 13

7.5714 7

7.9079 6

Expected Observed

7.5714 10

6.8984 4

6.7302 8

=S (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

Bar Graph

0

2

4

6

8

10

12

14

16

Mustard

Green

Scarlet

Peacock

Plum

White

Revolver

Poison

Wrench

Lead Pipe

Candlestick

Dagger

Rope

Weapon

Occ

urre

nces

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

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

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

Application

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

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