##### Question

In: Statistics and Probability

# A die is rolled 50 times and the following are the outputs: 6 1 3 4...

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?

## Solutions

##### Expert Solution

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.

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