Question

Part 2
Consider the following data set:

	Republican	Democrat	Independent	Total
Supports the death penalty	120	103	18
Opposes the death penalty	70	57	20
Does not know/Not sure	45	24	11
Total

1. Complete the table.
2. Calculate the expected frequencies.
3. Test whether the two variables are associated (dependent). State the hypotheses.
4. Perform an appropriate test of hypotheses. Report the test statistic, p-value, and make a decision. Copy and paste relevant test results.

(e) Interpret the p-value. Be sure to answer the research question.

Answer 1

(a) The completed is as below

Observed
	Republican	Democrat	Independent	Total
Supports	120	103	18	241
Opposes	70	57	20	147
Not Sure	45	24	11	80
Total	235	184	49	468

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(b) The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 468

The degrees of freedom, df = (r – 1) * (c -1) = (3 - 1) * (3 - 1) = 4

Expected
	Republican	Democrat	Independent	Total
Supports	121.015	94.752	25.233	241
Opposes	73.814	57.795	15.391	147
Not Sure	40.171	31.453	8.376	80
Total	235	184	49	468

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(c) The Hypothesis:

H0: There is no association between political party and stand on the death penalty. They are independent.

Ha: There is a relation between political party and stand on the death penalty. They are dependent.

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(d) The Test Statistic: The table below gives the calculation of .

#	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	120	121.015	-1.015	1.030225	0.0085
2	70	73.814	-3.8141	14.54736	0.1971
3	45	40.171	4.8291	23.32021	0.5805
4	103	94.752	8.2479	68.02785	0.7180
5	57	57.795	-0.7949	0.631866	0.0109
6	24	31.453	-7.453	55.54721	1.7660
7	18	25.233	-7.2329	52.31484	2.0733
8	20	15.391	4.609	21.24288	1.3802
9	11	8.376	2.6239	6.884851	0.8220
Total					7.557

test = 7.56

The p value: The p value at test = 7.56, df = 3; P value = 0.1091

The Decision Rule: If p value is < 0.05 (the default level), Then Reject H0.

The Decision: Since p value is > 0.05, Fail to Reject H0.

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(e) The probability of finding a test statistic as great as or greater than 7.56 Assuming that the null hypothesis is true is 0.1091, which is very high and therefore we fail to reject the null hypothesis.

There isn't sufficient evidence at the 95% level of significance to warrant rejection of the claim that there is a relation between political party and stand on the death penalty.

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