Every week, the Florida Lottery draws six numbers between 1 and 49. Lottery tick

Question

Every week, the Florida Lottery draws six numbers between 1 and 49. Lottery ticket buyers are naturally interested in whether certain numbers are drawn more frequently than others. To assist players, the Sun-Sentinel publishes the number of times each of the 49 numbers has been drawn in the past 52 weeks. The numbers and the frequency with which each occurred were recorded. a. If the numbers are drawn from a uniform distribution, what is the expected frequency for each number? b. Can we infer that the data were not generated from a uniform distribution?

Number Frequency 1 5 2 6 3 7 4 5 5 3 6 5 7 12 8 8 9 8 10 5 11 6 12 7 13 9 14 3 15 5 16 4 17 9 18 7 19 5 20 10 21 6 22 5 23 2 24 8 25 5 26 8 27 5 28 6 29 8 30 6 31 6 32 4 33 6 34 5 35 8 36 12 37 5 38 8 39 4 40 6 41 9 42 9 43 8 44 5 45 5 46 2 47 6 48 10 49 6

Explanation / Answer

as probability of each number fo uniform distribution =1/49

therefore expected frequency for each cell =total observations/49 =312/49 =6.37

applying chi square goodness of fit test on above:

here test stat =38.2244

degree of freedom =number of categories -m--1=47

for above p value =0.8155

as p value is very high we can not reject that above distribution follows uniform distribution,

we can not infer that the data were not generated from a uniform distribution

observed Expected Chi square Type Probability O E=total*p =(O-E)^2/E 1 1/49 5.000 6.37 0.29 2 1/49 6.000 6.37 0.02 3 1/49 7.000 6.37 0.06 4 1/49 5.000 6.37 0.29 5 1/49 3.000 6.37 1.78 6 1/49 5.000 6.37 0.29 7 1/49 12.000 6.37 4.98 8 1/49 8.000 6.37 0.42 9 1/49 8.000 6.37 0.42 10 1/49 5.000 6.37 0.29 11 1/49 6.000 6.37 0.02 12 1/49 7.000 6.37 0.06 13 1/49 9.000 6.37 1.09 14 1/49 3.000 6.37 1.78 15 1/49 5.000 6.37 0.29 16 1/49 4.000 6.37 0.88 17 1/49 9.000 6.37 1.09 18 1/49 7.000 6.37 0.06 19 1/49 5.000 6.37 0.29 20 1/49 10.000 6.37 2.07 21 1/49 6.000 6.37 0.02 22 1/49 5.000 6.37 0.29 23 1/49 2.000 6.37 3.00 24 1/49 8.000 6.37 0.42 25 1/49 5.000 6.37 0.29 26 1/49 8.000 6.37 0.42 27 1/49 5.000 6.37 0.29 28 1/49 6.000 6.37 0.02 29 1/49 8.000 6.37 0.42 30 1/49 6.000 6.37 0.02 31 1/49 6.000 6.37 0.02 32 1/49 4.000 6.37 0.88 33 1/49 6.000 6.37 0.02 34 1/49 5.000 6.37 0.29 35 1/49 8.000 6.37 0.42 36 1/49 12.000 6.37 4.98 37 1/49 5.000 6.37 0.29 38 1/49 8.000 6.37 0.42 39 1/49 4.000 6.37 0.88 40 1/49 6.000 6.37 0.02 41 1/49 9.000 6.37 1.09 42 1/49 9.000 6.37 1.09 43 1/49 8.000 6.37 0.42 44 1/49 5.000 6.37 0.29 45 1/49 5.000 6.37 0.29 46 1/49 2.000 6.37 3.00 47 1/49 6.000 6.37 0.02 48 1/49 10.000 6.37 2.07 49 1/49 6.000 6.37 0.02 1 312 312 38.2244

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