2. In a large clinic located in an inner city hospital, 56 patients with non-symptomatic HIV infection have been treated with an experimental drug believedto have the capability of restoring certain immune system functions associatedwith HIV infection. Of these patients, 12 had CD4 cell counts below 250 at theinitial visit, 20 had counts between 250 and 400, and 24 had counts above 400.(The lower the count, the worse the prognosis.) It is desired to take a stratifiedrandom sample of 30 patients, 10 from each of the three groups describedabove, for purposes of estimating the 12-month incidence of AIDS-definingevents among these patients. The results of this sample survey are shownbelow:Number of PersonsCD4 Level250-399220a. How many samples of 30 patients taken as described above are possible?b. Estimate the proportion of patients having one or more AIDS-definingevents.c. What is the estimated standard error of this estimated proportion?d. A simple random sample (without stratification) of 30 of these patientsyielded the following data:Number of Events0123Number of Events01232< 2506722N511< 2503102Number of PersonsCD4 Level250-3998210400 and Over91O400 and Over12010i. How many samples of size 30 are possible under simple randomsampling without stratification?ii. Estimate the incidence of AIDS-defining events from these dataand the estimated standard error of this estimated proportion.iii. Compare this with the results obtained from the stratified samplingdesign. Which design produces the more reliable estimate? Whydoes it?

2. In a large clinic located in an inner city hospital, 56 patients with non- symptomatic HIV infection have been treated with an experimental drug believed to have the capability of restoring certain immune system functions associated with HIV infection. Of these patients, 12 had CD4 cell counts below 250 at the initial visit, 20 had counts between 250 and 400, and 24 had counts above 400. (The lower the count, the worse the prognosis.) It is desired to take a stratified random sample of 30 patients, 10 from each of the three groups described above, for purposes of estimating the 12-month incidence of AIDS-defining events among these patients. The results of this sample survey are shown below: 1

2. In a large clinic located in an inner city hospital, 56 patients with non- symptomatic HIV infection have been treated with an experimental drug believed to have the capability of restoring certain immune system functions associated with HIV infection. Of these patients, 12 had CD4 cell counts below 250 at the initial visit, 20 had counts between 250 and 400, and 24 had counts above 400. (The lower the count, the worse the prognosis.) It is desired to take a stratified random sample of 30 patients, 10 from each of the three groups described above, for purposes of estimating the 12-month incidence of AIDS-defining events among these patients. The results of this sample survey are shown below: 1

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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