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A patron suspects a casino of using a weighted die (a die where every face is no

ID: 3160608 • Letter: A

Question

A patron suspects a casino of using a weighted die (a die where every face is not equally likely to come up). To investigate this, a statistician is brought in. The statistician rolls the suspect die 100 times, and records the number of times that each face (1 through 6) comes up. The results are below: You will use a chi-square goodness of fit test to evaluate the claim. Please do this by hand and show your work. You may use R to check your answer. State appropriate null and alternative hypotheses. Compute the expected counts. Then compute the observed test statistic, the appropriate degrees of freedom, and a p-value for the test. Make a conclusion in the context of the problem. Do you think the die is weighted? If so, how do you think it is weighted?

Explanation / Answer

Null hypothesis: The die is not weighted.

Alternate hypothesis: The die is weighted.

b).

Expected value =100/6=16.6667

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

18

16.667

1.333

0.107

24

16.667

7.333

3.227

13

16.667

-3.667

0.807

11

16.667

-5.667

1.927

18

16.667

1.333

0.107

16

16.667

-0.667

0.027

100

100.000

0.000

6.200

6.20

chi-square

5

df

P=0.2872

c).

Calculated P=0.2872 >0.05 level.

The null hypothesis is not rejected.

We conclude that the die is not weighted.

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

18

16.667

1.333

0.107

24

16.667

7.333

3.227

13

16.667

-3.667

0.807

11

16.667

-5.667

1.927

18

16.667

1.333

0.107

16

16.667

-0.667

0.027

100

100.000

0.000

6.200

6.20

chi-square

5

df

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