Question

You are conducting a multinomial hypothesis test (αα = 0.05) for the claim that all 5 categories are equally likely to be selected.

Category	Observed Frequency
A	14
B	19
C	11
D	8
E	21

What is the chi-square test-statistic for this data?
χ2=χ2=

What are the degrees of freedom for this test?
d.f. =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =  

Answer 1

Hypothesis:

Ho: All categories are equally likely to be selected

Ha: All 5 categories are Not equally likely to be selected

Total of Observed Frequencies are = 14+ 19 + 11 + 8 + 21 = 73

Expected Frequency of each category = 73/5 = 14.6 category

Computational Table:

	Oi	Ei	(Oi-Ei)	(Oi-Ei)2	(Oi-Ei)2/Ei
	14	14.6	-0.6	0.36	0.025
	19	14.6	4.4	19.36	1.326
	11	14.6	-3.6	12.96	0.888
	8	14.6	-6.6	43.56	2.984
	21	14.6	6.4	40.96	2.805
Total	73	73			8.027

Test statistic:

Degrees of Freedom (d.f) = k-1 = 5-1 = 4

Where, K = Number of Categories = 5

P-value: 0.0906 ...........................(Using Chi square Table)

P-value > , i.e 0.0906 > 0.05, That is Fail to Reject Ho at 5% level of significance.

Therefore, All categories are equally likely to be selected