Question

A die is rolled 50 times and the following are the outputs:

6 1 3 4 2 6 3 5 1 3 6 1 6 6 3 3 6 5 2 4 1 6 5 3 1 2 5 2 1 2 4 1 4 1 5 5 6 6 2 1 1 2 5 6 5 5 6 3 1 3

What is the p-value of the chi-square test that the die is unbiased?

Answer 1

Solution:

Test statistic formula for chi square test is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

The calculation table for the above test statistic is given as below:

Outcome	O	E	(O - E)^2/E
1	11	8.333333	0.853333333
2	7	8.333333	0.213333333
3	8	8.333333	0.013333333
4	4	8.333333	2.253333333
5	9	8.333333	0.053333333
6	11	8.333333	0.853333333
Total	50	50	4.24

Chi square = ∑[(O – E)^2/E]

Chi square = 4.24

Test statistic = 4.24

We are given

N = 6 outcomes

Degrees of freedom = df = N – 1 = 6 – 1 = 5

So, required p-value for this test by using chi square table or excel is given as below:

P-value = 0.515404429

P-value = 0.5154

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that die is unbiased.