With a perfectly balanced roulette wheel, in the long run, red numbers should tu

Question

With a perfectly balanced roulette wheel, in the long run, red numbers should turn up 18 times in 38. To test its wheel, one casino records the result of 3,800 plays, finding 1,890 red numbers. Is that too many reds? Or chance variation?

(a) Formulate the null and alternative hypothesis as statements about a box model.

(b) The null says that the percentage of reds in the box is _______. The alternative says that the percentage of reds in the box is ________. Fill in the blanks.

(c) Compute z and P.

(d) Were there too many reds?

Explanation / Answer

Ho: p=18/38
H1: p18/38

Test statistic: z = (p_hat - p)/sqrt(p(1-p)/n) = (1890/3800 - 18/38)/sqrt((18/38)*(1-18/38)/3800) = 2.92

p-value = 2* z(2.92) = 2*0.0017 = .0034

Reject Ho since p-value is less than =0.05.

The sample indicates that there were too many reds.

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