Question

A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 285 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	120	108	57
Left	45	36	14

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

(a) Find the expected number of people with no complaint who leave the HMO:

(b) Find the expected number of people with a medical complaint who leave the HMO:

(c) Find the expected number of people with a nonmedical complaint who leave the HMO:

(d) Find the test statistic:

(e) Find the degrees of freedom:

(f) Find the critical value:

Answer 1

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ha?: Some of the population proportions differs.

(a) the expected number of people with no complaint who leave the HMO: 95*1/3=31.667

(b) the expected number of people with a medical complaint who leave the HMO:95*1/3=31.667

(c) the expected number of people with a nonmedical complaint who leave the HMO:95*1/3=31.667

(d) The Chi-Squared statistic is computed as follows:

(e) the degrees of freedom:df=3?1=2.

(f) the critical value: Based on the information provided, the significance level is ?=0.01, the number of degrees of freedom is df = 3 - 1 = 2, The critical value is

(g) Since it is observed that , it is then concluded that the null hypothesis H0 is rejected.