Question

A student rolled a supposedly fair die 60 times, resulting in the distribution of dots shown. Research question: At α = .10, can you reject the hypothesis that the die is fair?

	Number of Dots
	1	2	3	4	5	6	Total
Frequency	9	16	11	12	6	6	60

Calculate the chi-square test statistic, degrees of freedom and the p-value. (Round your test statistic value to 2 decimal places and the p-value to 4 decimal places.)

Answer 1

Probability(Proportion) of getting any one of the 1 to 6 is 1/6

Ho: Die is fair i.e. p1=p2=p3=p4=p5=p6=1/6

So we have

Number of Dots	Observed Frequency	P	Expected Frequency(n*p)
1	9	1/6	10
2	16	1/6	10
3	11	1/6	10
4	12	1/6	10
5	6	1/6	10
6	6	1/6	10
Total	n=60	1	60

Degrees of freedom = Number of category -1=6-1 = 5

We will use Ti84

Enter Observed Frequency in L1 And Expected frequency in L2

Then Press STAT...TESTS...X^2 GOF -Test...

Enter values as

Result is

Test Statistic = 7.40

P-Value = 0.1926

P-Value > α=0.10

So we fail to reject the hypothesis that die is fair.