Chapter 11.2, Problem 45E

To determine

To perform hypothesis testing.

Answer to Problem 45E

There is convincing evidence that there is an association between age and opinion about loan-free tuition in the population of U.S. adults.

Explanation of Solution

Given:

		Age
		18-34	35-49	50-64	65+
Response	Support	91	161	272	332
	Oppose	25	74	211	255
	Don't know	4	13	20	51

The null and alternative hypotheses:

  $H_0$ : There is no association between age and response.

  $H_a$ : There is association between age and response.

Using excel,

		18-34	35-49	50-64	65+	Total
Support	Observed	91	161	272	332	856
	Expected	68.07	140.68	285.33	361.91	856.00
	(O - E)² / E	7.72	2.93	0.62	2.47	13.75
Oppose	Observed	25	74	211	255	565
	Expected	44.93	92.86	188.33	238.88	565.00
	(O - E)² / E	8.84	3.83	2.73	1.09	16.49
Don't know	Observed	4	13	20	51	88
	Expected	7.00	14.46	29.33	37.21	88.00
	(O - E)² / E	1.28	0.15	2.97	5.11	9.52
Total	Observed	120	248	503	638	1509
	Expected	120.00	248.00	503.00	638.00	1509.00
	(O - E)² / E	17.85	6.91	6.32	8.67	39.75
		39.75	chi-square
		6	df
		5.09E-07	p-value

Chi-square test statistic = 39.75. The degrees of freedom = 6 and p-value = 0.

Decision: P-value < 0.05, reject H0.

Conclusion: There is convincing evidence that there is an association between age and response.