Question

The contingency table below shows the results of a random sample of 200 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliations.

Test the claim of independence. Use α = .05.

Answer 1

Answer:

Here iam assuming the missing data to solve this problem

here we will use chi-square test of independence

let H0 : opinion on a bill are related to their party affiliation

Ha : opinion on a bill are not related to their party affiliation

using excel >phstat> chi square test we have

Observed Frequencies
	opinion			Calculations
party	Approve	Dispprove	No opinion	Total		fo-fe
Republician	42	20	14	76		3.24	-2.8	-0.44
Democrat	50	24	18	92		3.08	-3.6	0.52
Independent	10	16	6	32		-6.32	6.4	-0.08
Total	102	60	38	200
Expected Frequencies
	opinion
party	Approve	Dispprove	No opinion	Total		(fo-fe)^2/fe
Republician	38.76	22.8	14.44	76		0.270836	0.34386	0.013407
Democrat	46.92	27.6	17.48	92		0.202182	0.469565	0.015469
Independent	16.32	9.6	6.08	32		2.447451	4.266667	0.001053
Total	102	60	38	200
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	3
Degrees of Freedom	4
Results
Critical Value	9.487729
Chi-Square Test Statistic	8.03049
p-Value	0.090468
Do not reject the null hypothesis

Since calculated value 8.03049 is less than 9.487729 so we do not reject Ho and conclude that  opinion on a bill are related to their party affiliation

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