Senske’s First Block AP Statistics Alesha Seternus and Jenna Rorer

Objective: Be the first player to reach the Candy Castle by landing on the multi-colored rainbow space at the end of the path.

Sixty-four cards in a deck: 36 single-colored cards 22 double-colored cards 6 character cards The card colors consist of red, orange, yellow, green, blue, and purple The characters are Grandma Nutt, Mr. Mint, Jolly, Gingerbread, Lolly, and Princess Frostine

We have chosen the Chi-Squared Test in order to examine the following probabilities… Test One: The Probability of Choosing a Single- Colored Card from the Deck Test Two: The Probability of Choosing a Double- Colored Card from the Deck Test Three: The Probability of Choosing a Character Card from the Deck

Test One: The Probability of Choosing a Single Colored Card from the Deck Hypothesis: Ho:The observed frequency distribution for picking a single colored card fits the specified distribution Ha: The observed frequency distribution for picking a single colored card does not fit the specified distribution Assumptions: State: SRS Sample size large enough that all expected values are greater than or equal to 5 Check: Assumed Refer to chart

Trial RedPurpleYellowBlueOrangeGreen

TrialExpected Value Observed Value

Test One:The Probability of Choosing a Single-Colored Card from the Deck   obs-exp) 2 = exp ( ) 2 + ( ) = p(> ) = 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 the observed frequency distribution for picking a single colored card fits the specified distribution. df (k-1) = 29

Test Two: The Probability of Choosing a Double- Colored Card from the Deck Hypothesis: Ho:The observed frequency distribution for picking a single colored card fits the specified distribution Ha: The observed frequency distribution for picking a single colored card does not fit the specified distribution Assumptions: State: SRS Sample size large enough that all expected values are greater than or equal to 5 Check: Assumed Refer to chart

RedPurpleYellowBlueOrangeGreen

TrialExpected Value Observed Value

Test Two: The Probability of Choosing a Double- Colored Card from the Deck   (obs-exp) 2 = ( )2 + ( )2 + … exp = p( > ) = 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 the observed frequency distribution for picking a single colored card fits the specified distribution df (k-1) = 29

Test Three: The Probability of Choosing a Character Card from the Deck Hypothesis: Ho:The observed frequency distribution for picking a character card fits the specified distribution Ha: The observed frequency distribution for picking a character card does not fit the specified distribution Assumptions: State: SRS Sample size large enough that all expected values are greater than or equal to 5 Check: Assumed Refer to chart

Trial Gingerbr ead Mr. Mint JollyPrincess Frostine Gramma Nutt Lolly

TrialExpected Value Observed Value

Test Three: The Probability of Choosing a Character Card from the Deck =  (obs-exp) 2 = ( ) 2 + ( ) 2 + … exp p( > ) = = Conclusion: We fail to reject Ho in favor Ha because our P-value is greater than alpha (0.05). We have sufficient evidence that the observed frequency distribution for picking a character card fits the specified distribution. df (k-1) = 29

Personal Opinions/ Conclusions Bias/Error Our experiment was conducted through random samplings of the 64 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. If the 30 trials happened to be played by separate groups, all groups had to collect data under identical conditions. We have come to the conclusion that the probabilities of picking either a single-colored, double-colored, or character card is similar to the expected values.