Every week the Florida Lottery draws six numbers between 1 and 49. Lottery ticke
ID: 3304723 • Letter: E
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.
Using excel, can you show what formulas you use.
Data is listed below.
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
Number Observed Frequency Expected frequency (Observed - Expected)^2/Expected 1 5 6 0.166666667 2 6 6 0 3 7 6 0.166666667 4 5 6 0.166666667 5 3 6 1.5 6 5 6 0.166666667 7 12 6 6 8 8 6 0.666666667 9 8 6 0.666666667 10 5 6 0.166666667 11 6 6 0 12 7 6 0.166666667 13 9 6 1.5 14 3 6 1.5 15 5 6 0.166666667 16 4 6 0.666666667 17 9 6 1.5 18 7 6 0.166666667 19 5 6 0.166666667 20 10 6 2.666666667 21 6 6 0 22 5 6 0.166666667 23 2 6 2.666666667 24 8 6 0.666666667 25 5 6 0.166666667 26 8 6 0.666666667 27 5 6 0.166666667 28 6 6 0 29 8 6 0.666666667 30 6 6 0 31 6 6 0 32 4 6 0.666666667 33 6 6 0 34 5 6 0.166666667 35 8 6 0.666666667 36 12 6 6 37 5 6 0.166666667 38 8 6 0.666666667 39 4 6 0.666666667 40 6 6 0 41 9 6 1.5 42 9 6 1.5 43 8 6 0.666666667 44 5 6 0.166666667 45 5 6 0.166666667 46 2 6 2.666666667 47 6 6 0 48 10 6 2.666666667 49 6 6 0 2 = 41.66666667 Degrees of freedom = 48 p- value = 0.728521909 Ho: The data comes from a uniform distribution Ha: The data does not come from a uniform distribution Since 0.7285 > 0.05, we fail to reject the null hypothesis Conclusion: There is not enough evidence that the data does not come from a uniform distribution.
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