2. A patron suspects a casino of using a weighted die (a die where every face is

Question

2. 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 Face | Frequency 18 24 16 100 Total 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. (a) State appropriate null and alternative hypotheses. (b) Compute the expected counts. Then compute the observed test statistic, the appropriate degrees of freedom, and a p-value for the test. (c) Make a conclusion in the context of the problem. Do you think the dic is weightod? If so, how do you think it is weighted?

Explanation / Answer

Ho: p1= p2 = ..p6

Ha: not Ho

expected count = 100/6 = 16.666

TS = 6.2 , df= r-1 = 5

p-value = 0.2872

as p-value > 0.05

we fail to reject the null , we think the die is not weighted

p Oi Ei (Oi-Ei)^2/Ei 0.166667 18 16.6666667 0.106666667 0.166667 24 16.6666667 3.226666667 0.166667 13 16.6666667 0.806666667 0.166667 11 16.6666667 1.926666667 0.166667 18 16.6666667 0.106666667 0.166667 16 16.6666667 0.026666667 1 100 100 6.2 critical value 11.07049769

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