Question

# You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4...

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

 #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

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