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

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

4. 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

5. 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

6. 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

7. Trial RedPurpleYellowBlueOrangeGreen 1643155 4454432 3311211 4111111 5350443 6315245 7425421 84611753 9442144 10322345 11724553 12043233 13564566 14235422 15364848 16641634 17424444 18524165 19533211 20342223 21325385 22223938 23978455 24356243 25353323 26866566 27243423 28637655 29333413 30221132

8. TrialExpected Value Observed Value 123.62524 221.937522 311.81259 411.256 520.812519 620.2520 718.562518 831.536 919.687519 1018.019 1123.62526 1214.62515 1332.62532 1416.87518 1531.533 1625.312524 1720.812524 1824.7523 1914.62515 2014.62516 2123.062526 2228.12527 2336.562528 2424.7523 2516.312519 2635.437537 2720.2518 2833.187532 2918.017 3011.812511

10. Test One:The Probability of Choosing a Single-Colored Card from the Deck   obs-exp) 2 = exp (24-23.625) 2 + (22-21.9375) 2 +... 23.625 21.9375 = 8.7155 p(> 8.7155) = 0.9999019051 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

11. 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

12. RedPurpleYellowBlueOrangeGreen 13 2 3 2 1 3 4 0 2 5 4 2 32 1 3 2 1 0 1 3 4 5 0 2 4 5151 2 4 3 2 6 3 1 2 7 3 2 1 4 0 4 8 3 3232 9 1 3 0 2 3 1 10 3 1 11 4 2 3 2 0 1 2 12 1 4 1 2 13 4 1 4 2 4 1 3 2 14 1 5 2 3 15 5 2 4 3 0 16 5 2 1111 4 2 17 3 5 1 2 3 18 4 1 4 3 1 19 1 2 0 2 1 2 20 1 3 0 2 21 4 3 1 4 2 1 22 7 4 0 1 236 2 3 4 2 3 2 24 4 1 3 1 1 25 2 4 3 5 1 4 26 4 2 27 2 5 3 2 3 28 3 6 4 1 3 29 5 1 2 2 30 3 1 1 0

13. TrialExpected Value Observed Value 114.43817 213.40615 37.218810 46.87512 512.71914 612.37514 711.34412 819.2518 912.03112 1011.011 14.43814 128.9378 1319.93821 1410.3139 1519.2521 1615.46817 12.71912 1815.12518 198.93759 208.93758 2114.09414 2217.18817 2322.34421 2415.12517 259.96889 2621.65621 2712.37513 2820.28121 2911.013 307.21888

15. Test Two: The Probability of Choosing a Double- Colored Card from the Deck   (obs-exp) 2 = (17-14.438)2 + (15-13.406)2 + … exp 14.438 13.406 = 8.26496 p( > 8.26496) = 0.9999441532 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

16. 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

17. Trial Gingerbr ead Mr. Mint JollyPrincess Frostine Gramma Nutt Lolly 1100010 2001010 3001010 4000110 5101101 6100010 7100101 8111000 9011111 10100000 11000110 12001001 13111101 14000011 15011001 16011110 17100011 18000011 19011010 20000011 21011100 22011211 23011121 24011011 25000001 26111210 27111011 28100211 29100001 30000200

18. TrialExpected Value Observed Value 13.93751 23.3656352 31.968752 41.8752 53.468754 63.3752 73.093753 85.252 93.281255 103.02 113.93752 122.43753 135.43755 142.81253 155.252 164.218754 173.468753 184.1253 192.43752 202.43752 213.843752 224.68756 236.093756 244.1254 252.718751 265.906256 273.3755 285.531256 293.02 301.96882

20. Test Three: The Probability of Choosing a Character Card from the Deck =  (obs-exp) 2 = (1-3.9375) 2 + (2-3.65625) 2 + … exp 3.9375 3.6525 p( >14.0230261) = 0.99126 =14.0230261 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

21. 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.