Part 2 of 4(b) Find the P-value. Round the answer to four decimal places.The P-value is 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 ofnumbered 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 142 drawingswere 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 isfair, then the winning number is equally likely to occur in any category. Following are the observed frequencies. Test thehypothesis that each of the categories is equally likely. Use the 0.10 level of significance and the P-value method with the TI-84Plus calculator.Category 1-7 8-14Observed3720Send data to Excel15-21 22-28 29-35212539

The data on power state (multistate lottery) which is divided in 5 category is,CategoryObserved1-7378-142015-212122-282529-3539Total Sum142The N=142 represents the sum of the Observed frequency.level of significance = 0.10The test hypothesis is,H0: P1=P2=P3=P4=P5=1/5 (i.e. each of the categories is equally likely.)Vs H1: The some or all probability differs from 1/5.the test statistic is χ2 =where O is the observed frequency, and E is the expected frequency.Now calculate the expected frequencyE= expected probability N That each of the categories is equally likely means each group probability = 1/5 =0.2the expected frequency for each group is,CategoryExpected frequency (E)1-70.2×142 =28.4 8-140.2×142 =28.415-210.2×142 =28.422-280.2×142 =28.429-350.2×142 =28.4Total Sum142now calculate the test statistic value,CategoryOEO-E(O-E)2(O-E)2/E1-73728.48.6 73.962.60428-142028.4 -8.470.562.484515-212128.4 -7.454.761.928222-282528.4 3.4 11.560.407029-353928.410.6 112.363.9563 Sum11.3803The test statistic value is,χ2 = 11.3803Now calculate p-valuep-value = P(χ2>χ2statistic) Where χ2 is the following chi-square distribution with (no of Category-1) degree of freedom i.e Df=4 P-value = 1-P(χ2<χ2statistic) = 1-CHISQ.DIST(11.3803,4,TRUE)........(using Excel function) = 1- 0.9774 = 0.0226The p-value is 0.0226.The p-value is 0.0226.