A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 423 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 177 111 135 Left 64 27 50 If the null hypothesis is Ho : P = p2 = p, and using a = 0.05, then do following: (a) Find the expected number of people with no complaint who leave the HMO: 59 (b) Find the expected number of people with a medical complaint who leave the HMO: 37 (c) Find the expected number of people with a nonmedical complaint who leave the HMO: 45 (d) Find the test statistic: (e) Find the degrees of freedom: () Find the critical value:

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 423 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
177
111
135
Left
64
27
50
If the null hypothesis is Ho : p1 = P2 = P3 and using a = 0.05, then do the following:
(a) Find the expected number of people with no complaint who leave the HMO: 59
(b) Find the expected number of people with a medical complaint who leave the HMO: 37
(c) Find the expected number of people with a nonmedical complaint who leave the HMO: 45
(d) Find the test statistic:
(e) Find the degrees of freedom:
(f) Find the critical value:
(g) The final conclusion is
O A. We can reject the null hypothesis that the proportions are equal.
O B. There is not sufficient evidence to reject the null hypothesis.
Transcribed Image Text:A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 423 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 177 111 135 Left 64 27 50 If the null hypothesis is Ho : p1 = P2 = P3 and using a = 0.05, then do the following: (a) Find the expected number of people with no complaint who leave the HMO: 59 (b) Find the expected number of people with a medical complaint who leave the HMO: 37 (c) Find the expected number of people with a nonmedical complaint who leave the HMO: 45 (d) Find the test statistic: (e) Find the degrees of freedom: (f) Find the critical value: (g) The final conclusion is O A. We can reject the null hypothesis that the proportions are equal. O B. There is not sufficient evidence to reject the null hypothesis.
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