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A casino customer is concerned about whether the dice the casino are using are \

ID: 3155931 • Letter: A

Question

A casino customer is concerned about whether the dice the casino are using are "fair" (i.e., each face is equally likely to appear). The customer obtains a die that is being used by the casino and rolls it 240 times. The customer records the following data:

a) Compute the value of the test statistic.

b) X^2 = ______________

c) Set up the appropriate rejection region for a(alpha) = 0.10.

d) Reject H_o when X^2 > ______________.

e) What is the appropriate conclusion?

f) We ______________ conclude that the die is fair.

Face 1 2 3 4 5 6 Frequency 46 38 44 45 38 29

Explanation / Answer

a)

If it is fair, we expect 240/6 = 40 on each.

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
46   40   0.9  
38   40   0.1  
44   40   0.4  
45   40   0.625  
38   40   0.1  
29   40   3.025  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    5.15   [ANSWER]

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b)

chi^2 = 5.15 [ANSWER]

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c)  
          
As df = a - 1,           
          
a =    6      
df = a - 1 =    5      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      

chi^2(crit) =    11.07049769      

Hence, reject Ho when chi^2 > 11.070.

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d)

Hence, reject Ho when chi^2 > 11.070.
          
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e)

As 5.15 < 11.070, we fail to reject Ho.

f)

We CAN conclude that the die is fair. [ANSWER]

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