Question 138793: 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.
Digit Frequency
0 33
1 17
2 25
3 30
4 31
5 28
6 24
7 25
8 32
9 25
Total 270
Perform the chi-square test for a
uniform distribution. At α = .05, can you reject the hypothesis that the digits are from a uniform
population?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
Digit Frequency
0 33
1 17
2 25
3 30
4 31
5 28
6 24
7 25
8 32
9 25
Total 270
Perform the chi-square test for a uniform distribution. At α = .05, can you reject the hypothesis that the digits are from a uniform population?
Ho: digits are from a uniform population
Ha: digits are not from a uniform population
------------
The listed numbers are the Observed values. If the results were
from a uniform distribution the Expected values would each be
(1/10)*270 = 27
--------------------
Running a Chi-Sq test with a TI calculator I get:
Test Statistic: Chi-Sq = 4.15563...
p-value = 0.901
------------------
Conclusion: Since the p-value is greater than 5%, Fail to Reject Ho.
The observed results are statistically speaking from a uniform
distribution.
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Cheers,
Stan H.
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