Question

A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 420 patients was taken. Data was collected on whether a patient had filed a complaint and, if so, whether the complaint was medical or nonmedical in nature. After a year, a tally from these patients was collected to count number who left the HMO voluntarily. Here are the data on the total number in each group and the number who voluntarily left the HMO:

	No complaint	Medical complaint	Nonmedical complaint
Total	180	96	144
Left	58	41	41

If the null hypothesis is H0:p1=p2=p3 and using α=0.01, then do the following:

(d) Find the test statistic:

Answer 1

Solution :-

Given data:

	No complaint	Medical complaint	Non-medical complaint
Total	180	96	144
Left	58	41	41

Here we have to find out the Test statistic.

It is a chi-square test statistic.

Here we know the formula,  

Now consider the table to complete the test statistics.

	No complaint	Medical complaint	Non-medical complaint	Total
Left	58	41	41	140
Not left	= (180 -58) = 122	= (96 - 41) = 55	= (144 - 41) = 103	280
Total	180	96	144	420

Now we have to find out the expected frequencies.

	Expected Frequencies (E)
	No complaint	Medical complaint	Non-medical complaint	Total
Left	= (180 * 140) / 420 = 60	= (96 * 140) / 420 = 32	= (144 * 140) / 420 = 48	140
Not left	= (180 * 280) / 420 = 120	= (96 * 280) / 420 = 64	= (144 * 280) / 420 = 96	280
Total	180	96	144	420

Now consider the table to calculate Chi-square test statistic.

Observed Frequencies (O)	Expected Frequencies (E)
58	60	= 0.06666
41	32	= 2.53125
41	48	= 1.02083
122	120	= 0.03333
55	64	= 1.26562
103	96	= 0.5104

Test statistic is