Question

Roulette Refer to Exercise 2.

a. Confirm that the expected counts are large enough to use a chi-square distribution to calculate the P-value. What degrees of freedom should you use?

b. Use Table C to find the P-value. Then use your calculator’s χ2 cdf command.

c. What conclusion would you draw about whether or not the roulette wheel is operating correctly?

Short answer

Part (a) The $df=2$

Part (b) The $P-$value$=0.1108$

Part (c) There isn't enough evidence to refute the claim concerning the probability distribution in question.

Step-by-step solution

Part (a) Step 1: Given information

Color	Observed count	Frequency	Expected count
Red	85	0.47	94.74
Black	99	0.47	94.74
Green	16	0.05	10.53
Total	200	1.00	200

The chi-square test statistic $=4.04$

Part (a) Step 2: Calculation

The projected counts are large enough to use a chi-square distribution if all predicted counts are at least $5$This condition is satisfied.

The degrees of freedom $=df=c-1=3-1=2$

Part (b) Step 1: Given information

The chi-square test statistic $=4.04$

The degrees of freedom $=2$

Part (b) Step 2: Calculation

The $p-$value using table for $df=2$ is,

$0.10<P<0.15$

The excel formula, $=CHIDIST(4.40,2)$

$P-$value $=0.1108$

Part (c) Step 1: Given information

The chi-square test statistic $=4.04$

The degrees of freedom $=2$

The $p-$value$=0.1108$

Part (c) Step 2: Calculation

Here, $p-value>0.05$fail to reject $H_0$

There isn't enough evidence to refute the claim concerning the probability distribution in question.