Question

# #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)

#### Homework Answers

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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