Question

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A political researcher wishes to know if political affiliation and age are related. He has collected data on 409 persons in three age categories. Is there evidence that age and political affiliation are related?

Age	Democrat	Republican	Independent	Total
18-31	61	57	34	152
32-51	59	63	29	151
52-68	40	43	23	106
Total	160	163	86	409

Step 1: State the null and alternative hypothesis.

H0H0: political affiliation and age are dependent

HaHa: political affiliation and age are independent OR

H0H0: political affiliation and age are independent

HaHa: political affiliation and age are dependent

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

Ans:

1)

H0: political affiliation and age are independent

Ha: political affiliation and age are dependent.

2)

expected value for the number of democrats that are 18-31 years old=160*152/409=59.5

3)

expected value for the number of independents that are 32-51 years old=86*151/409=31.8

4)

	Observed(fo)
Age	Democrat	Republican	Independent	Row Total
18-31	61	57	34	152
32-51	59	63	29	151
52-68	40	43	23	106
Column Total	160	163	86	409
	Expected(fe)
Age	Democrat	Republican	Independent	Row Total
18-31	59.5	60.6	32.0	152
32-51	59.1	60.2	31.8	151
52-68	41.5	42.2	22.3	106
Column Total	160	163	86	409
	Chi square=(fo-fe)^2/fe
Age	Democrat	Republican	Independent	Row Total
18-31	0.040	0.211	0.130	0.381
32-51	0.000	0.132	0.238	0.371
52-68	0.052	0.014	0.023	0.088
Column Total	0.092	0.357	0.391	0.840

Test statistic:

Chi square=0.840

5) degrees of freedom=(3-1)*(3-1)=4

6)critical value=CHIINV(0.05,4)=9.488

7)As,test statistic is less than critical value,so

Fail to reject the null hypothesis