Question

In order to receive credit for the homework, you must show all steps for doing a chi square test of independence. These steps include: null and alternative hypothesis); critical value; calculations (show work); reject or accept H; results statement using no relationship or a relationship. A random sample of 500 voters were selected and asked their opinion on tax reform. The sample was further divided into Democrats and Republicans. The following table gives the results of the poll. At a 0.05 is there a relationship between opinion and voting 1. reference? Indifferent Opposed Favor 83 138 64 Democrat Republican 64 67 84

Answer 1

The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 500

Observed
	Favor	Indifferent	Opposed	Total
Democrat	138	83	64	285
Republican	64	67	84	215
Total	202	150	148	500
Expected
	Favor	Indifferent	Opposed	Total
Democrat	115.1400	85.5000	84.3600	285
Republican	86.8600	64.5000	63.6400	215
Total	202	150	148	500

The degrees of freedom (df): df = (r - 1) * (c - 1) = (2 - 1) * (3 - 1) = 1 * 2 = 2

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The Hypothesis:

H0: There is no relation between opinion and voting reference.

Ha: There is a relation between opinion and voting reference.

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The Critical Value:   The critical value at $\alpha$ = 0.05, df = 2

$\chi^2$critical = 5.992

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The Test Statistic: The table below gives the calculation of $\chi^2$ .

Number	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	138	115.140	22.860	522.580	4.539
2	64	86.860	-22.860	522.580	6.016
3	83	85.500	-2.500	6.250	0.073
4	67	64.500	2.500	6.250	0.097
5	64	84.360	-20.360	414.530	4.914
6	84	63.640	20.360	414.530	6.514
			Total		22.15247

$\chi^2$test = 22.15

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The p value: The p value at $\chi^2$ test = 22.15, df = 2 is;p value = 0.000

The Decision Rule: If $\chi^2$ test is > $\chi^2$ critical, then Reject H0.

Also, If p value is < $\alpha$ then reject H0.

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The Decision:    Since If $\chi^2$ test (22.15) is > $\chi^2$ critical (5.992), We Reject H0.

Also since p value (0.0000) is < $\alpha$ (0.05), We Reject H0.

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The Conclusion: There is sufficient evidence at the 95% significance level to conclude that there is a relation between opinion and voting reference.

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