A die is said to be fair if the probability of rolling the n

A die is said to be fair if the probability of rolling the number i is pi=1/6 for i=1,…,6. You roll a die 60 times with the following outcome.

(a) Calculate the test statistic X2 for the test

using the formula

X2=(OiEi)2Ei.

X2= ______

(b) Use the R function pchisq() and the value of the test statistic from (a) to find the p-value for the test in (a).

p-value = ______

Solution

A)

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
15   10   2.5  
9   10   0.1  
9   10   0.1  
10   10   0  
6   10   1.6  
11   10   0.1  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    4.4   [ANSWER]

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b)

As df = a - 1,           
          
a =    6      
df = a - 1 =    5      
          
Thus, the p value is          
          
p =    0.493373524   [ANSWER]