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I L7 1' \\V " U PSYNS I AmmdM Egon. Fli D MonanUiiiveimy Indianapolis PERFORM A CHI-SQUARE GOODNESS 0F FIT: The Hoosier Lottery scratchoff game titled "Lady Luck" costs $5 00 and, according to hoosierlottery.com, has a 1 in 3.94 odds of winning. Imagine we bought 10 of these scratch-off tickets, Follow the steps below to perform a Chi-Squa re Goodness of Fit test to say whether we won as many times as you'd expect based on the published odds of Winning. 7. Based on the advertised 1 in 3.94 odds of winning, how many ofthe 10 games purchased would you expect to be Winners and how many would you expect to be losers (Le, what is our \"expected count" for number of Winning cards and losing cards)? Do not round to whole numbers, 0 Expected count for winning scratch-offs: 0 Expected count for losing scratch-offs: 8. Imagine we scratch off all 10 games and find that only 1 card is a winner and 9 cards were not, Is the Hoosier Lottery lying about the odds of winning? Use the expected counts (obtained above) with the observed counts (provided here to solve for 2 using the formula below. Circle your final answer (obtained 7}). X X2 = Z ((0 13W 9. Use the formula below to calculate the effect size (Phi, (D) of this 12. Z =i~ 10. Would you describe the size of this effect as small, medium, or large? a. Small b. Medium c. Large 11, Assuming an alpha level of .05, look up the critical ChiSquared statistic from Appendix C, Table E. For this example, our degrees of freedom is just the number of categories (two: win vs. loss) minus 1. Thus, we have one degree of freedom. Use the critical )6 to decide whether to reject or retain the null hypothesis. a Critical 7:1: . Should we reject or retain the null hypothesis? a) We should reject the null hypothesis; the model does not do an accurate Job predicting number of Winning scratch of tickets. b) We should retain the null hypothesis; the model accurately predicts the number of Winning scratch of tickets. w