Question

A student in a statistics class tossed a die 300 times and obtained the results shown in the table. Is the die fair? In other words does it fit a uniform distribution? Let alpha =.05        

Outcome	1	2	3	4	5	6
Observed Frequency	53	41	60	47	38	61

A. What is the null hypothesis?

B. What is the alternative hypothesis?

C. What distribution are you using?

D. What test are you running?

E. What is your conclusion?

Answer 1

A) null hypothesis : all the outcomes are equally likely :or probability of each outcome on die =1/6

B) alternative hypothesis :at least one outcome has different probability to appear .

C) Chi square distribution

D) chi square goodness of fit test:

degree of freedom =categories-1=			5
for 0.05 level and 5 degree of freedom :rejection region =				11.070

Applying 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	53.000	50.000	0.42	0.180
2	1/6	41.000	50.000	-1.27	1.620
3	1/6	60.000	50.000	1.41	2.000
4	1/6	47.000	50.000	-0.42	0.180
5	1/6	38.000	50.000	-1.70	2.880
6	1/6	61.000	50.000	1.56	2.420
total	1.000	300	300		9.2800

test statistic X² =9.28

E) as test statisitc is not in critical region we can not reject null hypothesis

we can not conclude that die is biased