Question

A political researcher wishes to know if political affiliation and age are related. He has collected data on 510510persons in three age categories. Is there evidence that age and political affiliation are related?

Age	Democrat	Republican	Independent	Total
18-31	66	74	34	174
32-51	66	59	36	161
52-68	68	75	32	175
Total	200	208	102	510

Step 2: Find the expected value for the number of democrats that are 18-31 years old. Round your answer to one decimal place. (E18-31 and democrat=)

Step 3: Find the expected value for the number of independents that are 32-51 years old. Round your answer to one decimal place. (E32-51 and independent=)

Step 4: Find the value of the test statistic. Round your answer to three decimal places.

Step 5: Find the degrees of freedom associated with the test statistic for this problem.

Step 6: Find the critical value of the test at the 0.05 level of significance. Round your answer to three decimal places.

Step 7: Make the decision to reject or fail to reject the null hypothesis at the 0.05 level of significance. (Fail to reject the null hypothesis or reject the null hypothesis)

Answer 1

Observed Frequencies
Age	Democrat	Republican	Independent	Total
18-31	66	74	34	174
32-51	66	59	36	161
52-68	68	75	32	175
Total	200	208	102	510
Expected Frequencies
	Democrat	Republican	Independent	Total
18-31	200 * 174 / 510 = 68.2353	208 * 174 / 510 = 70.9647	102 * 174 / 510 = 34.8	174
32-51	200 * 161 / 510 = 63.1373	208 * 161 / 510 = 65.6627	102 * 161 / 510 = 32.2	161
52-68	200 * 175 / 510 = 68.6275	208 * 175 / 510 = 71.3725	102 * 175 / 510 = 35	175
Total	200	208	102	510
	(fo-fe)²/fe
18-31	(66 - 68.2353)²/68.2353 = 0.0732	(74 - 70.9647)²/70.9647 = 0.1298	(34 - 34.8)²/34.8 = 0.0184
32-51	(66 - 63.1373)²/63.1373 = 0.1298	(59 - 65.6627)²/65.6627 = 0.6761	(36 - 32.2)²/32.2 = 0.4484
52-68	(68 - 68.6275)²/68.6275 = 0.0057	(75 - 71.3725)²/71.3725 = 0.1844	(32 - 35)²/35 = 0.2571

Null and Alternative hypothesis:

Ho: Political affiliation and age are not related.

H1: Political affiliation and age are related.

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Step 2: =

Expected value for the number of democrats that are 18-31 years old = 200 * 174 / 510 = 68.2

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Step 3:

Expected value for the number of independents that are 32-51 years old = 102 * 161 / 510 = 32.2

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4. Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 1.9230

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5. df = (r-1)(c-1) = 4

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6. Critical value:

χ²α = CHISQ.INV.RT(0.05, 4) = 9.488

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7. Decision:

p-value > α, fail to reject the null hypothesis.