Question

A roulette wheel has 38 slots along its circumference labeled 00, 0, 1, . . . , 36. In the game of roulette, the wheel is spun around and then a ball is dropped in its center. Bets are placed on where the ball will settle once the wheel has stopped spinning. If the wheel is properly balanced, then every slot has an equal chance of being landed on. After a trip to a local casino, your friend swears that the roulette wheel there is unbalanced. She seems to think that the ball lands on the number 15 slot more often than any others. To test her claim you go to the casino and discretely observe 350 spins. You observe that the balls lands on the number 15 on 40 of those spins.

(b)(T9) Is there sufficient evidence to support your friend’s claim?

Answer 1

H0:Null Hypothesis:P = 1/38 = 0.0263

HA: Alternative Hypothesis: P > 0.0263

n = 350

$\hat{p}$ = 40/350 = 0.1143

P = 0.0263

Q = 1 - P = 0.9737

SE = $\sqrt{PQ/n}$

$=\sqrt{0.0263\times 0.9737/350}=0.0086$

Test statistic is:
Z = (0.1143 - 0.0263)/0.0086 = 10.2326

Take $\alpha$ = 0.05

From Table, critical value of Z = 1.645

Since the calculated value of Z is greater than critical value of Z, the difference is significant. Reject null hypothesis.

Conclusion:

There is sufficient evidence to support friend's claim.