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 29Explanation / 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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