#2) A sixsided 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 
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, chisquare = 13.597
n  6 
alpha  0.05 
degrees of freedom  5 
pvalue  0.0184 
Critical value  11.07 
Fail to reject null hypothesis
The die is fair
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