In a three-digit lottery, each of the three digits is supposed to have the same

Question

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 shows the frequency of occurrence of each digit for 90 consecutive daily three-digit drawings.

    

Calculate the chi-square test statistic, degrees of freedom, and the p-value. (Perform a uniform goodness-of-fit test. Round your test statistic value to 2 decimal places and the p-value to 4 decimal places.)

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 shows the frequency of occurrence of each digit for 90 consecutive daily three-digit drawings.

Explanation / Answer

for above:

   Test statistic =17.48

df =number of categories -1 =10-1 =9

p value =0.0417

observed Expected Chi square digits Probability O E=total*p =(O-E)^2/E 0 1/10 20.000 27.00 1.81 1 1/10 22.000 27.00 0.93 2 1/10 34.000 27.00 1.81 3 1/10 21.000 27.00 1.33 4 1/10 26.000 27.00 0.04 5 1/10 15.000 27.00 5.33 6 1/10 29.000 27.00 0.15 7 1/10 35.000 27.00 2.37 8 1/10 35.000 27.00 2.37 9 1/10 33.000 27.00 1.33 1 270 270 17.4815

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