Question

Determine​ (a) the χ2 test​ statistic, (b) the degrees of​ freedom, (c) the critical value using alpha equals 0.05α=0.05​, and​ (d) test the hypothesis at the alpha equals 0.05α=0.05 level of significance.

Ho:Pa=Pb=Pc=Pd=1/4

H1​: At least one of the proportions is different from the others.

Outcome	A	B	C	D
Observed	52	47	53	48
Expected	50	50	50	50

Answer 1

Ho:Pa=Pb=Pc=Pd=1/4

H1​: At least one of the proportions is different from the others.

observed frequencey, O		expected frequency,E	(O-E)		(O-E)²/E
52		50.00	2.00		0.080
47		50.00	-3.00		0.180
53		50.00	3.00		0.180
48		50.00	-2.00		0.080

chi square test statistic,X² = Σ(O-E)²/E =   0.520              
                  
level of significance, α=   0.05              
Degree of freedom=k-1=   4   -   1   =   3
                  
Critical value =    7.815   [ Excel function: =chisq.inv.rt(α,df) ]

Decision:test stat < critical value, Do not reject Ho             

so,there is not enough evidence to say taht   At least one of the proportions is different from the others.

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