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	17
B	11
C	24
D	25
E	25

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

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
A	0.200	17	20.40	-0.75	0.567
B	0.200	11	20.40	-2.08	4.331
C	0.200	24	20.40	0.80	0.635
D	0.200	25	20.40	1.02	1.037
E	0.200	25	20.40	1.02	1.037
total	1.000	102	102		7.608

chi-square test-statistic X² =7.608

degree of freedom =categories -1=5-1=4

p value =0.1070