A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 360 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:

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 25PPS
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A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 360 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 159 132 69
Left 60 34 26


If the null hypothesis is H0:p1=p2=p3 and using α=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:

 

 

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