21. Is the lottery fair? Mega which players try to guess the numbers that will turn up in a drawing of numbered balls. One of the balls drawn is the Mega Ball. Matching the number drawn on the Mega Ball increases ones winnings. During a recent three-year period, the Mega Bal was drawn from a collection of 15 balls numbered 1 through 15 and a total of 344 drawings were made. For the purposes of this exercise, we grouped the numbers into five categories: 1-3, 4-6. 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. Category 1-3 4-6 7-9 10-12 13-15 Observed 73 64 74 62 71 Source: www.usamega.com a. Compute the expected frequencies. b. Compute the value of x c. How many degrees of freedom are there? d. Test the hypothesis that each of the categories is equally likely. Use the a = 0.05 level of significance.

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