Maryland lottery. For a lottery to be successful, the public must have confidence in its fairness. One of the lotteries in Maryland is Pick-3 Lottery, where 3 random digits are drawn each day.8 A fair game depends on every value (0 to 9) being equally likely at each of the three posi- tions. If not, then someone detecting a pattern could take advantage of that and beat the lottery. To investigate the randomness, we'll look at data collected over a recent 32-week period. Although the winning numbers look like three-digit numbers, in fact, each digit is a randomly drawn numeral. We have 654 random digits in all. Are each of the digits from 0 to 9 equally likely? Here is a table of the frequencies.
|
Group
|
Count
|
%
|
|
0
|
62
|
9.480
|
|
1
|
55
|
8.410
|
|
2
|
66
|
10.092
|
|
3
|
64
|
9.786
|
|
4
|
75
|
11.468
|
|
5
|
57
|
8.716
|
|
6
|
71
|
10.856
|
|
7
|
74
|
11.315
|
|
8
|
69
|
10.550
|
|
9
|
61
|
9.327
|
a) Select the appropriate procedure.
b) Check the assumptions.
c) State the hypotheses.
d) Test an appropriate hypothesis and state your results.
e) Interpret the meaning of the results and state a conclusion.