You are conducting a multinomial Chi-Square Goodness of Fit hypothesis test for the claim that the 4

rasigapr6

rasigapr6

Answered question

2022-03-09

You are conducting a multinomial Chi-Square Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: H0: pA=0.3,pB=0.1; pC=0.1; pD=0.5
Complete the table. Report all answers accurate to three decimal places.
 Category  Observed Frequency  Expected Frequency  A 24 B 12 C 7 D 44
What is the chi-square test-statistic for this data?
χ2=
What is the P-Value?
P-Value=

Answer & Explanation

chupablew20

chupablew20

Beginner2022-03-10Added 1 answers

The expected values are,
 Category  Observed Frequency  Proportion  Expected Frequency  A 240.387×0.3=26.1 B 120.187×0.1=8.7 C 70.187×0.1=8.7 D 440.587×0.5=43.5
The chi-square test-statistic is,
χ2=(OE)2E
=(2426.12}{26.1}+(128.7)28.7+(78.7)28.7+(4443.5)243.5
=0.169+1.252+0.332+0.006
=1.759
Thus, the chi-square test-statistic is 1.759.
The degrees of freedom is,
df=k-1
=4-1
=3
The degrees of freedom is 3.
Computation of P-value:
The P-value of χ2-distribution for test statistic 1.759 at 3 degrees of freedom can be obtained using the excel formula “=CHISQ.DIST.RT(1.759,3)”. The P-value is 0.624.
Thus, the P-value is 0.624.

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