Question

A six-sided die is thrown 50 times. The numbers of occurrences of each face are shown below.

Face	1	2	3	4	5	6
Count	12	9	8	9	7	5

Can you conclude that the die is not fair?  Determine the type of test should be used in this situation and the test statistic.

	a.	Goodness of Fit,
	b.	Goodness of Fit,
	c.	Two sample z-test for proportions, z = 1.138
	d.	One sample z-test for proportions, z = 1.391
	e.	Test for Indepdence,

Answer 1

As we are testing here whether the frequency of each number on the dice is equally likely, therefore this is a goodness of fit test for the 6 numbers which is a chi square test. Therefore a goodness of fit test ( a chi square test is the correct answer here)

The expected frequency for each of the 6 faces here is computed as:
E_i = 50/6 = 25/3

Therefore the chi square test statistic now is computed here as:

Therefore 3.28 is the chi square test statistic value here.

For k - 1 = 5 degrees of freedom, the p-value here is obtained from the chi square distribution tables as:

As the p-value here is 0.6569 which is very very high, therefore the test is not significant here and therefore we dont have sufficient evidence here that the dice is not fair.