Question

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

HoHo : pA=0.1pA0.1;  pB=0.5pB0.5;  pC=0.3pC0.3;  pD=0.1pD0.1

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

Category	Observed Frequency	Expected Frequency
A	23
B	54
C	37
D	8

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

What is the P-Value?
P-Value =  


For significance level alpha 0.01,

What would be the conclusion of this hypothesis test?

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

Answer 1

#observed frequency				chi square    χ2
Category	#observed frequency	Expected	Expected %	=(Oi-Ei)2/Ei
A	23	12.2	0.1	9.560655738
B	54	61	0.5	0.803278689
C	37	36.6	0.3	0.004371585
D	8	12.2	0.1	1.445901639
total	122	122	1	11.81420765

Expected frequency=Expected%*total=Expected%*122

chi square    χ2 =(Oi-Ei)2/Ei =11.814

P_value=P(χ2(df=3)>11.812)=0.008

For significance level alpha 0.01,

P-value< 0.01 hence we reject Null hypothesis