Question

Is the lottery fair? Power ball is a multistate lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. One of the balls drawn is the "Powerball." Matching the number drawn on the Powerball increases one's winnings. In a 17 month period, the Power ball was drawn from a collection of 35 balls numbered 1 through 35. A total of 146 drawings were made. For the purpose of this exercise, we grouped the numbers in to five categories: 1-7, 8-14, and so on. If the lottery is fair, then the winning number is equally likely to occur in any category. Following are the observed frequencies. Test the hypothesis that each of the categories is equally likely. Use the 0.025 level of significance and the P-value method with the TI-84 Plus calculator. Category 1-7 Observed 40 Send data 8-14 20 15-21 22-28 29-35 37 21 28 Y to Excel Part: 0 / 4 Part 1 of 4 (a) State the null and alternate hypotheses. HO:P, P2=P3-P4-Ps= U H, Some or all of the actual probabilities (Choose one) from those specified by H.

Answer 1

(a)There are 5 categories in total. Under the null hypothesis, each category is likely to contain same number of observations. So, each observation is equally likely to belong to each of the 5 categories. So, the null hypothetical value of the probabilities is = 1/5 = 0.2

The null and alternative hypotheses are:

H0: p1 = p2 = p3 = p4 = p5 = 0.2 against

H1: Some or all of the actual probabilities is different from those specified by H0.