For Exercises 1–4, perform the goodness of fit test.
Question 11.78
marylandlott
3. Truly Random Lottery Drawing? Have you ever wondered whether lottery drawings are truly random? For example, the accompanying histogram shows the frequencies of the third digit in the Maryland lottery's Pick 3 game (218 drawings from September 1989 to April 1990). In a Pick 3 game, you choose a three-digit number between 000 and 999, and if your number comes up, you win the cash prize. Notice that 1 appears as the third digit least of all the digits, and quite a bit less often than some of the other digits. Does the relative scarcity of 1s indicate that the system is flawed?
The relative frequency distribution of the third digit is shown in the following table. We would, of course, expect each digit to show up 10% of the time. Test whether the population proportions of digits are all 0.10, using level of significance .
| Digit | Count | Percent |
|---|---|---|
| 0 | 26 | 11.93 |
| 1 | 12 | 5.50 |
| 2 | 26 | 11.93 |
| 3 | 18 | 8.26 |
| 4 | 23 | 10.55 |
| 5 | 19 | 8.72 |
| 6 | 18 | 8.26 |
| 7 | 27 | 12.39 |
| 8 | 30 | 13.76 |
| 9 | 19 | 8.72 |
| 218 |
11.99.3
, , , , , , , , , . : Not all the proportions in are equal. Reject if -value . , , , , , , , , , . Since none of the expected frequencies is less than 1 and none of the expected frequencies is less than 5, the conditions for performing the goodness of fit test are met. Reject if -value . . -value . Since the -value is not , we do not reject . There is insufficient evidence that the population proportions of digits are not all 0.10.