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...

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 141 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 0.05 level of significance and the P-value method with the TI-84 Plus calculator.