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Chapter 11: Q 6. (page 716)

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

Expert verified

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

01

Part (a) Step 1: Given information

ColorObserved countFrequencyExpected count
Red850.4794.74
Black990.4794.74
Green160.0510.53
Total2001.00200

The chi-square test statistic =4.04

02

Part (a) Step 2: Calculation

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

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

03

Part (b) Step 1: Given information

The chi-square test statistic =4.04

The degrees of freedom =2

04

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

05

Part (c) Step 1: Given information

The chi-square test statistic =4.04

The degrees of freedom =2

The p-value=0.1108

06

Part (c) Step 2: Calculation

Here, p-value>0.05fail to reject H0

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

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