Question

Suppose that you are the manager of a casino and you collect data on one of your roulette tables. You find that among the last 10,000 bets, there were only 350 bets for which a red or black number did not win. On average, you expect the proportion of winning bets for black or red to equal p=18/19.

a) Compute a 95% confidence interval for the proportion of winning black or red bets.

b) Conduct a two-sided hypothesis test (α=0.05)for HO: p=18/19. State the relevant p-value and your decision whether to reject or not reject HO.

c) Compare your results in part (a) and (b). Are they consistent?

Answer 1

given data and some calculations are:-

sample size (n) = 10000

sample proportion () = (10000-350)/10000 = 9650/10000 = 0.965

a).z critical value for 95% confidence level, both tailed test be:-

the 95% confidence interval for the proportion of winning black or red bets is:-

b).hypothesis:-

test statistic be:-

p value :-

decision:-

p value = 0.000 < 0.05 (alpha)

so, we reject the null hypothesis .

c).decision based on confidence interval :-

as the hypothesized proportion 18/19 or 0.947368 is not included in the 95% confidence interval.i.e, in (0.961,0.969) , we reject the null hypothesis.

so, we can say that results in part (a) and (b) are consistent.

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