Question

A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 273 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 the 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: 63 Medical complaint: 132 Nonmedical complaint: 78 Left: No complaint: 26 Medical complaint: 53 Nonmedical complaint: 12 If the null hypothesis is H0: p1 = p2 = p3 and using Î± = 0.01, then do the following: (Use two decimal places when appropriate) (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:

          A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 273 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 the 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: 63
Medical complaint: 132
Nonmedical complaint: 78

Left:
No complaint: 26
Medical complaint: 53
Nonmedical complaint: 12

If the null hypothesis is H0: p1 = p2 = p3 and using Î± = 0.01, then do the following: (Use two decimal places when appropriate)

(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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Added by Carmen H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sri K

05/29/2023

Step 1

Step 1:** Calculate the expected number of people with no complaint who leave the HMO: Expected number = (Total number with no complaint * Total number who left) / Total number of patients Expected number = (63 * 26) / 273 Expected number = 6 ** Show more…

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A certain health maintenance organization (HMO) wishes to study why patients leave the HMO. A SRS of 273 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 the 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: 63 Medical complaint: 132 Nonmedical complaint: 78 Left: No complaint: 26 Medical complaint: 53 Nonmedical complaint: 12 If the null hypothesis is H0: p1 = p2 = p3 and using Î± = 0.01, then do the following: (Use two decimal places when appropriate) (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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Transcript

00:01 Now in this question we have to find the total number of the members who left hmo.

00:08 Okay, so the total number of person who left hmo is 41 people who didn't have any complaint, 70 people who have medical complaints and 43 people who have non -medical complaints.

00:33 So this is total of 154.

00:36 Then total number of people in sample shown is actually 147 people with no complaint, 192 people with medical complaint and 123 people with non -medical complaint.

00:58 So a total of 462 complaints.

01:01 Now expected number of people who left the group, who left the hmo, okay, left hmo for no complaints would be equal to 147 divided by 462 multiplied by 154 and that is equal to 49.

01:45 So this is the solution for part a.

01:48 For part b, left hmo with medical complaints and this is equal to 192 divided by 462 multiplied by 154.

02:17 And this comes out to be 63 .94.

02:23 And this is the solution for part b of our question.

02:27 Coming to the part c, who left hmo for non -medical complaints.

02:41 Okay, so this would be equal to 123 divided by 462 multiplied by 154.

02:55 And this is equal to 41 .04.

03:00 And this is the solution for the part c of our question.

03:02 Now moving to the part d of the question, the test statics.

03:08 Now, the test statics is given by the summation of observed subtracting from expected whole square and whole divided by the expected...

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