Problem: For a lottery to be successful, the public must have confidence in its fairness. One of the lotteries in a state is a pick-3 lottery, where 3 random digits are drawn each day. A fair game depends on every value (0 to 9) being equally likely at each of the three positions. If not, then someone detecting a pattern could take advantage of that and beat the lottery. To investigate the randomness, we'll look at the data collected over a 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. Is each of the digits from 0 to 9 equally likely? A table of the frequencies is shown to the right. Complete parts a through e.
|
Group
|
Count
|
%
|
|
0
|
62
|
9.480
|
|
1
|
57
|
8.716
|
|
2
|
64
|
9.789
|
|
3
|
66
|
10.092
|
|
4
|
75
|
11.468
|
|
5
|
56
|
8.563
|
|
6
|
72
|
11.009
|
|
7
|
74
|
11.315
|
|
8
|
67
|
10.245
|
|
9
|
61
|
9.327
|
1. State the hypotheses
2. Test an appropriate hypothesis and state your results.
3. Compute the P-value for the test.