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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