Class Note for PUBHLTH 540 at UMass(9)
Class Note for PUBHLTH 540 at UMass(9)
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Date Created: 02/06/15
Puleth 540 Introductory Biostatistics Page 1 of 3 Unit 6 Estimation Week 10 Practice Problems Due Monday December 1 2008 l Betore you begin This exercise is a straightforward con dence interval calculation for a binomial proportion See lecture notes pp 6064 andor textpp 205206 An entomologist samples a field for egg masses ofa harmful insect by placing a yard square frame at random locations and carefully examining the ground within the frame A simple random sample of 75 locations selected from a county s pasture land found egg masses in 13 locations Compute a 95 confidence interval estimate of all possible locations that are infested Betore you begin This exercise is NOT a mimicking of the lecture notes It is asking you to start your thinking from the WIDTH of a con dence interval and then reason your solution from there Have a look at the lecture notes page 21 See also textpp 187194 Alzheimers disease has a poorer prognosis when it is diagnosed at a relatively young age Suppose we want to estimate the age at which the disease was first diagnosed using a 90 con dence interval Under the assumption that the distribution of age at diagnosis is normal if the population variance is 6285 how large a sample size is required if we want a con dence interval that is 10 years wide Betore you begin In this exercise you get practice in combining the ideas of estimation in unit 6 and the z score methods thatyou learned in unit 5 In unit 6 see page 46 In unit 5 see page 19 The National Health and Nutrition Examination Survey of 19751980 give the following data on serum cholesterol levels in US males Age Population Mean Population Standard Deviation Group years 11 6 1 2024 180 43 2 2534 199 49 Suppose the distribution of serum cholesterol is normal in each age group If you draw simple random samples of size 50 from each of the two groups what is the probability that the difference between the two sample means Group 2 mean 7 Group 1 mean will be more than 25 Source National Center or Health Statistics R Fulwood W Kalsbeek B Rifkind et al Total serum cholesterol levels ofadults 20 74 years ofage United States 19761980 Vital and Health Statistics Series II No 236 DHHS Pub No PHD 861686 Public Health Service Washington DC US Government Printing O ice May 1986 Citedin Daniel p 140 5 41 Copyright 1999 by John Wiley amp Sons Inc By permission ofJohn Wiley Wkl OJaracticedoc Puleth 540 Introductory Biostatistics Page 2 of 3 4 Betore you begin The solution to this exercise uses the same approach that is described on page 37 of the unit 6 lecture notes Also the example on page 38 Pages in the text are pp 199201 The objectives of a study by Kennedy and Bhambhani 1991 were to use physiological measurements to determine the testretest reliability of the Baltimore Therapeutic Equipment Work Simulator during three simulated tasks performed at light medium and heavy work intensities and to examine the criterion validity of these tasks by comparing them to real tasks performed in a controlled laboratory setting Subjects were 30 healthy men between the ages of 18 and 35 The investigators reported a standard deviation of s057 for the variable peak oxygen consumption lmin during one of the procedures Assuming normality compute a 95 con dence interval for the population variance for the oxygen consumption variable 5 Betore you begin This exercise draws from the material presented on pp 4044 of the unit 6 notes Because two measurements are made on each patient the data in this exercise are paired The purpose of an investigation by Alahuhta et al 1991 was to evaluate the in uence of extradural block for elective caesarian section simultaneously on several maternal and fetal hemodynamic variables and to determine if the block modi ed fetal myocardial function The study subjects were eight healthy parturient in gestational weeks 3842 with uncomplicated singleton pregnancies undergoing elective caesarian section under extradural anesthesia Among the measurements taken were maternal diastolic arterial pressure during two stages of the study The following are the lowest values of this variable at the two stages Compute a 95 con dence interval for the difference in diastolic blood pressure between the two stages Patient ID 1 2 3 4 5 6 7 8 Stage 1 70 87 72 70 73 66 63 57 Stage 2 79 87 73 77 80 64 64 60 Source Alahuhta S Rasanen J Jouppila R Jouppila P and Kangas Saarela T and Hoomen AI 1991 Uteroplacental and fetal hemoydynamics during extradural anesthesia for caesarian section British Journal ofAnesthesia 66 319323 Cited in Daniel p 248 743 Copyright 1999 by John Wiley amp Sons Inc By permission ofJohn Wiley Wkl Ojracticedoc Puleth 540 Introductory Biostatistics Page 3 of 3 6 Betore you begin The ideas and calculations pertaining to con dence intervals for the ratio of two variances is described in the lecture notes for unit 6 pp 5 759 SUGGESTION Use an F distribution calculator on the web This will spare you from having to use the formula on the bottom of page 55 A possible environmental determinant of lung function in children is the amount of cigarette smoking in the home To study this question two groups of children were studied Group 1 consisted of 23 nonsmoking children aged 59 both of whose parents smoke in the home Group 2 consisted f 20 nonsmoking children aged 59 neither of whose parents smoke The mean SD of FEBl for group 1 is 21 L 07 and for the Group 2 children the mean SD of FEVl is 23 L 04 Under the assumption of normality construct a 95 con dence interval for the ration of the variance of the two groups What is your conclusion regarding the reasonableness of the assumption of equality of variances 7 Betore you begin See lecture notes for unit 6 pp 4552 See also text pp 308310 For the same data in problem 6 and drawing upon your answer to 6 regarding the reasonableness of equality of variances compute a 95 con dence interval for the true mean difference in FEVl between 59 year old children whose parents smoke and comparable children whose parents do not smoke Wkl Ojracticedoc
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