Question

AN American roulette wheel contains, 38 slots: 18 red, 18 black, and 2 green. A casino has purchased a new wheel and they want to know if there is any evidence that the wheel is unfair. They spin the wheel 100 times and it lands on red 44 times, black 49 times, and green 7 times. Do a chi- square testing (goodness of fit) to see if we have sufficient evidence at 5% that the proportions are what is expected or not.

Answer 1

Since there are 18 slots out of 38 so probability that wheel stop on red slot is

P(red) = 18/38

Likewise

P(black) = 18/38

P(green) = 2/38

Following table shows the calculations for chi square test statistics:

O	p	E = p *100	(O-E)^2/E
44	18/38	47.3684	0.239529276
49	18/38	47.3684	0.056200306
7	2/38	5.2632	0.573125521
Total		100	0.868855102

Following is the test statistics:

Degree of freedom: df= 3-1 = 2

The p-value using excel function "=chidist(0.87, 2)" is: 0.6476

Since p-value is greater than 0.05 so there is sufficient evidence that  the proportions are as expected.