Question

A mental health service agency is conducting a study of how clients pay for the counseling services they receive. The agency accepts payment in one of four ways: in person, by mail, by credit card, or by third-party insurance. The agency randomly sampled 400 clients to determine if there is a relationship between the client’s age and the payment method used. The following sample results were obtained:

Counseling Service Payments

Payment Method	Age of Client
	20-30	31-40	41-50	Over 50
In Person	8	12	11	13
By Mail	29	67	72	50
By Credit Card	26	19	5	7
By Third-Party Insurance	23	35	17	6

Based on the sample data, can the agency conclude there is a relationship between the age of the client and the payment method used? Conduct the appropriate test at the α = 0.01 level of significance.

Answer 1

The chi-square statistic is 50.3155. The p-value is < 0.00001. The result is significant at p < .01.