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#2)   A six-sided die is rolled 120 times. The data in the following table shows the...

#2)   A six-sided die is rolled 120 times. The data in the following table shows the results for 120 rolls:

Number of dots facing up

     Frequency  

Expected frequency

           1

            15

           2

            29

           3

            16

           4          

            15

           5

            30

           6

            15
  1. Fill in the expected frequencies
  2. Use the data given to test the claim that the die is fair (i.e. that the probabilities for each value are the same)
Math   Statistics-And-Probability   
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Answer #1
Category pi Observed Freq. (Oi) Expected Freq. (Ei) (Oi - Ei)^2/Ei
1 0.1667 15 20.00 1.252
2 0.1667 29 20.00 4.046
3 0.1667 16 20.00 0.801
4 0.1667 15 20.00 1.252
5 0.1667 30 20.00 4.995
6 0.1667 15 20.00 1.252
120 13.597

test statistic, chi-square = 13.597

n 6
alpha 0.05
degrees of freedom 5
p-value 0.0184
Critical value 11.07

Fail to reject null hypothesis

The die is fair

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