Question

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:

Ho : pA=0.2;  pB=0.3;  pC=0.3; pD=0.2

Complete the table. Report all answers accurate to three decimal places.

Category	Observed Frequency	Expected Frequency
A	28
B	38
C	28
D	39

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

What is the P-Value?
P-Value =  


For significance level alpha 0.05,

What would be the conclusion of this hypothesis test?

• Reject the Null Hypothesis
• Fail to reject the Null Hypothesis

Report all answers accurate to three decimal places.

Answer 1

Ho : p_A=0.2;  p_B=0.3;  p_C=0.3; p_D=0.2

H₁ : The probabilities / proportions are not correct

Let the los be alpha = 5%

From the given data

	Observed		Expected
Category	Freq (Oi)	Prob	Freq Ei	(Oi-Ei)^2 /Ei
A	28	0.2	26.6	0.073684211
B	38	0.3	39.9	0.09047619
C	28	0.3	39.9	3.549122807
D	39	0.2	26.6	5.780451128
Total:	133		133	9.493734336

Num Categories: 4
Degrees of freedom: 3

Test Statistic, X^2: 9.494

P-Value: 0.0234

Here P-value < alpha (0.05) we reject H0

Correct answer:

• Reject the Null Hypothesis

Thus we conclude that the given probabilities / proportions are not correct