With a perfectly balanced roulette wheel, in thelong run, red numbers should tur

Question

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

(a) Formulate the null and alternative hypotheses as statementsabout 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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