Question

In a recent survey conducted by the Pew Research Center, a random sample of adults 18 years of age or older living in the continental united states was asked their reaction to the word socialism. In addition, the individuals were asked to disclose which political party they most associate with. Results of the survey are given in the table.

	Democrat	Independent	Republican
Positive	220	144	62
Negative	279	410	351

a) Explain why this data should be analyzed by the homogeneity of proportions.

b) Does the evidence suggest individuals within each political affiliation react differently to the word socialism? (Use the =0.05 level of significance.)

1. State the null and alternate hypothesis

2. Verify the requirements.

3. Calculate the test statistic.

4. Find the corresponding p-value.

5. State your conclusion.

Answer 1

ANSWER::

(a)

Because the variables are categorical.

(b)

The hypothesis being tested is:

H0: Individuals within each political affiliation react the same to the word socialism

Ha: Individuals within each political affiliation react differently to the word socialism

		Col 1	Col 2	Col 3	Total
Row 1	Observed	220	144	62	426
	Expected	145.00	160.98	120.01	426.00
	O - E	75.00	-16.98	-58.01	0.00
	(O - E)² / E	38.79	1.79	28.04	68.62
Row 2	Observed	279	410	351	1040
	Expected	354.00	393.02	292.99	1040.00
	O - E	-75.00	16.98	58.01	0.00
	(O - E)² / E	15.89	0.73	11.49	28.11
Total	Observed	499	554	413	1466
	Expected	499.00	554.00	413.00	1466.00
	O - E	0.00	0.00	0.00	0.00
	(O - E)² / E	54.68	2.53	39.53	96.73
		96.73	chi-square
		2	df
		9.88E-22	p-value

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that individuals within each political affiliation react differently to the word socialism.

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