Testing Fairness of Roulette Wheel A statistician observed 500 spins of a roulet

Question

Testing Fairness of Roulette Wheel A statistician observed 500 spins of a roulette wheel at the Mirage Resort and Casino. For each spin, the ball can land in any one of 38 different slots that are supposed to be equally likely. When STATDISK was used to test the claim that the slots are in fact equally likely, the test statistic X 2  X2 = 38.232 was obtained, also STATDISK displayed a P-value of 0.41331.

a. Find the critical value assuming that the significance level is 0.10 (using Table A-4).
Answer
b. Write a conclusion about the claim that the 38 results are equally likely.
We Answer evidence to support rejection of the claim. :

Explanation / Answer

The test statistic is 38.232 and significance level is 0.10.

There are 38 slots Therefore n = 38 and table A4 means chi Square table.

Therefore critical value = chi Square at level of significane 0.10 and degrees of freedom (df) = n - 1 = 38 - 1 = 37.

Using chi Square table critical value is 48.363.

b)

Test statistic is 38.232 < critical value 48.363 Therefore we do not reject the claim that 38 results are equally likely.

Therefore there is no evidance to support the claim.

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