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

Group Count %

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. Are 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

CO VOUTA WN -

64

9.786

8.257

9.939

9.633

11.315

57

8.716

70

10.703

11.009

11.468

9.174

a) Select the appropriate procedure.

What kind of chi-square test would be appropriate?

O A. Chi-square test for independence

O B. Chi-square test for homogeneity

C. Chi-square test for goodness-of-fit

O D. A chi-square test would not be appropriate

b) Check the assumptions. Are all of the assumptions and conditions satisfied? Select all that apply.

A. No, the randomization condition is not satisfied.

B. No, the counted data condition is not satisfied

C. No, the expected cell frequency condition is not satisfied.

YD. Yes, all of the assumptions and conditions are satisfied.

E. No, the independence assumption is not satisfied.

) State the hypotheses

Ho: The likelihood of drawing each numeral is equal.

HA: The likelihood of drawing each numeral is not equal.

d) Test an appropriate hypothesis and state your results.

Compute the appropriate test statistic.

The test statistic is

Round to three decimal places as needed.)

e) Interpret the meaning of the results and state a conclusion

f) Compute the P-Value for the Test