Question

A die was rolled 300 times. The following frequencies were recorded.

Outcome 1 2 3 4 5 6

Frequency 62 45 63 32 47 51

Do these data indicate that the die is unfair ? Use a 1% level of significance.

Answer 1

Null hypothesis: Ho: Die is fair ; each number occur with equal frequency

Alternate hypothesis: Ho: Die is unfair ; at least one number occur with different frequency.

degree of freedom =categories-1=			5
for 0.01 level and 5 df :crtiical value X2 =			15.086	from excel: chiinv(0.01,5)
Decision rule: reject Ho if value of test statistic X2>15.086

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
Category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	1/6	62	50.00	1.6971	2.8800
2	1/6	45	50.00	-0.7071	0.5000
3	1/6	63	50.00	1.8385	3.3800
4	1/6	32	50.00	-2.5456	6.4800
5	1/6	47	50.00	-0.4243	0.1800
6	1/6	51	50.00	0.1414	0.0200
total	1.00	300	300		13.4400
test statistic X2=		13.440

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence at 1% level to conclude that die is unfair,