Chapter 11.2, Problem 46E

To determine

To perform hypothesis testing.

Answer to Problem 46E

There is convincing evidence that there is an association between age and online banking for internet users.

Explanation of Solution

Given:

		Age
		18-29	30-49	50-64	65+
Online banking	Yes	265	352	304	167
	No	130	190	249	189

The null and alternative hypotheses:

  $H_0$ : There is no association between age and online banking.

  $H_a$ : There is association between age and online banking.

Using excel,

		18-29	30-49	50-64	65+	Total
Yes	Observed	265	352	304	167	1088
	Expected	232.81	319.45	325.93	209.82	1088.00
	(O - E)² / E	4.45	3.32	1.48	8.74	17.98
No	Observed	130	190	249	189	758
	Expected	162.19	222.55	227.07	146.18	758.00
	(O - E)² / E	6.39	4.76	2.12	12.54	25.81
Total	Observed	395	542	553	356	1846
	Expected	395.00	542.00	553.00	356.00	1846.00
	(O - E)² / E	10.84	8.08	3.59	21.28	43.80
		43.80	chi-square
		3	Df
		1.67E-09	p-value

Chi-square test statistic = 43.80. The degrees of freedom = 3 and p-value = 0.

Decision: P-value < 0.05, reject H0.

Conclusion: There is convincing evidence that there is an association between age andonline banking.