2) In a three-digit lottery, each of the three digits is supposed to have the sa

Question

2) In a three-digit lottery, each of the three digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). The table to the right summarizes the frequency of occurrence of each digit for 90 consecutive daily three-digit drawings. The table also appears in the Lottery worksheet of the HW12 data workbook on Moodle.

a) What is the appropriate null and alternate hypothesis to determine if the digits are not random?

b) Choose a level of Use = 0.05 for this problem.

c) Sketch the sampling distribution. Include the critical value and test statistic

d) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.

e) What is the p-value for the hypothesis test.

Digit fi: Observed 0 33 1 17 2 25 3 30 4 31 5 28 6 24 7 25 8 32 9 25 Total 270

Explanation / Answer

null hypothesis: digits are uniformly distributed in the data

alternate hypothesis: all digits are not uniformloy distributed

for above chi stat 7.70 and 9 degree of freedom ; p value =0.5643

as p value is higher then 0.05 level we can not reject null hypothesis.

observed Expected Chi square digits P O E=total*p =(O-E)^2/E 0 0.10 33 27.00 1.33 1 0.10 17 27.00 3.70 2 0.10 25 27.00 0.15 3 0.10 30 27.00 0.33 4 0.10 31 27.00 0.59 5 0.10 28 27.00 0.04 6 0.10 24 27.00 0.33 7 0.10 25 27.00 0.15 8 0.10 32 27.00 0.93 9 0.10 25 27.00 0.15 270 270 7.70

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