Question

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies Complete the table. Report all answers accurate to three decimal places Observed Expected Category Frequency Frequency A 51 B 30 С 137 D 41 What is the chi-square test-statistic for this data? What is the P-Value? P-Value- For significance level alpha 0.05, What would be the conclusion of this hypothesis test? O Fail to reject the Null Hypothesis O Reject the Null Hypothesis Report all answers accurate to three decimal places

Answer 1

The Complete table as

Category	Observed Frequency	Probability(P)	Expected frequency(P*N)
A	51	0.3	47.7
B	30	0.15	23.85
C	37	0.4	63.6
D	41	0.15	23.85
N=	159

Chi Square is calculated as

Using the data in Excel

Chi-Square is computed as

Category	Observed Frequency	Probability(P)	Expected frequency(P*N)	Residual(Obs-Exp)	(obs-exp)^2	{(Obs-Exp)}^2/Exp
A	51	0.3	47.7	3.3	10.89	0.228301887
B	30	0.15	23.85	6.15	37.8225	1.585849057
C	37	0.4	63.6	-26.6	707.56	11.12515723
D	41	0.15	23.85	17.15	294.1225	12.33218029
N=	159				Chi Square=	25.27148847

Hence, Chi square=25.272

c) P value associated with Chi Square is computed using Chi-square table as

P value=0.000014

10 00 (r-16 11 84 64 04 33 90 68 r 04 03 2 1 45 00001 12233 02000000 1122 250 0 0 122 r12345 67890

d) Conclusion:

Since P value<<0.05( level of significance) hence, reject the null hypothesis.