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statistical sampling to auditing
Sampling Of Populations Methods And Applications 4th Edition Paul S. Levy, Stanley Lemeshow - Solutions
Suppose that a simple random sample of five clusters is selected from the population shown in Exercise 10.16 and that the clusters selected 1 are 5, 8, 23, 30, and 36. Take a second-stage sample of 1 listing unit from each sample cluster, and estimate from this sample the mean number of admissions
A list of hospitals in a rural geographic area is shown in the accompanying table, by county. A sample survey is planned using a sample design in which counties are clusters, hospitals are listing units, and one hospital is to be selected from each county. If it is assumed that the total expenses
A household survey is to be conducted for purposes of estimating certain health status and health utilization variables. The survey research laboratory contracted to perform the study has access to U.S. Census Bureau lists of households and can define clusters of 18 households from which a sample
What would be the standard error of the estimated total number of patients given diazepam based on the cluster size n and number m of sample clusters determined in Exercises 10.12 and 10.13?
Based on the average cluster size calculated above, how many health centers should be sampled if one wishes to be 95% certain of estimating the number of patients given diazepam to within 10% of the true value?
A study was initiated having as a major objective estimation of the number of patients with severe trauma seen during the calendar year 2004 in hospitals not designated as trauma centers in urban counties in Illinois outside of the Chicago area which have both Trauma Centers (T) and hospitals not
Would the data shown in Exercise 10.8 indicate a high or a low intraclass correlation coefficient? State the reason for your answer, and verify it by computing the intraclass correlation coefficient.
If in Exercise 10.8, the cost associated with testing the units were 15 times that associated with listing and sampling the boxes, how many units should be sampled within each selected box?
A manufacturer of an orthopedic device would like to initiate a quality control program in which a sample of these devices would be sampled and tested for defects. After the units exit the assembly, they are grouped in batches of 20 boxes, with each box containing 10 units. It is desired to sample
Using the intraclass correlation coefficient calculated in Exercise 10.6, and assuming C" = 2C', what would be the optimal number of days to sample in a two-stage simple cluster sample with weeks as clusters?
From the population shown in Exercise 10.4, compute the intraclass correlation coefficient for the number of visitors to the park.
Suppose that a simple one-stage cluster sample was selected from the poplation shown in Exercise 10.4 and that clusters two and eight were selected.From this sample, compute the 95% confidence intervals for the characteristics given in parts (a)-(e) of Exercise 10.4.
Suppose that during the peak season the number of visitors to a state park and the number of injuries occurring among these visitors are as given in the accompanying table by week and day (the park is closed on Fridays).Suppose that a simple two-stage cluster sample was taken with weeks as
A simple random sample requires 400 listing units in order for estimated means and totals to meet specifications of precision. If all PSUs have the same number N of listing units, how large a simple cluster sample with cluster size n equal to 4 would be needed to achieve the same precision when the
Suppose that the elementary schools in a city were grouped into 30 school districts, with each school district containing ten schools. Suppose that a simple random sample of three school districts was taken and that within each sample school district a simple random sample of four schools was taken
Suppose that Chicago is divided into 75 community areas and that each community area contains 20 retail pharmacies. Suppose that you wish to estimate the average prices charged for some standard prescription drugs by taking a simple random sample of eight community areas followed by a simple random
For the sample survey of district courts discussed in an illustrative example in this chapter, draw a graph with the abscissa being total fixed costs and the ordinate being the coefficient of variation of the estimated total number of persons receiving treatment for substance abuse. The graph
Suppose that 40,000 person-hours were allotted for field costs for the sample survey of district courts discussed in an illustrative example in this chapter.Using the cost functions and cost components developed for this example, determine which of the two sample designs—simple one-stage cluster
In the situation described in Exercise 9.9, derive a simplified expression for the variance of an estimated ratio.
In many health science situations, a cluster consists of a pair of elements (e.g., in opthalmology, clusters might be patients; elements might be eyes, etc.). In this situation, derive a simplified expression for the variance of an estimated total.
In the scenario described in Exercise 9.7, it is anticipated that it would take about 15 min for a dentist to examine each quadrant, and that it would take approximately 20 min of clerical time to schedule the appointment for each patient sampled and to prepare the patient for the examination. If
A dental HMO has 368 members, and each member has four quadrants (upper left, upper right, lower left, lower right). It is desired to conduct a sample survey with the objective in mind of estimating the total number of quadrants among the membership that require some form of periodontal surgery.
In Exercise 9.5, it was discovered during the field work that sample neighborhood group 2 in District 3 no longer existed because of redistribution of the population. With this in mind, obtain modified estimates of the parameters estimated in Exercise 9.5.
A survey that used a simple one-stage cluster sampling design was conducted in a large city in China. The clusters in this instance were entities known as"neighborhood groups" (translated from the Chinese "jumin xiaozu"), which are essentially groups of contiguous households. These so-called
The number of beds in each of the ten hospitals sampled in Exercise 9.3 is shown in the accompanying table. The remaining 23 hospitals not appearing in the sample have a total of 3687 beds. Use this information to obtain improved estimates and confidence intervals for the following:a. The total
A simple one-stage cluster sample was taken of ten hospitals in a midwestern state from a population of 33 hospitals that have received state and federal funds to upgrade their emergency medical services. Within each of the hospitals selected in the sample, the records of all patients hospitalized
A sample of patients is to be taken from the patient records of a large psychiatric outpatient clinic for purposes of estimating the total number of patients given antidepressant drugs as part of their therapeutic regimen. The records are organized into file drawers, each containing 20 patient
Suppose that the elementary schools in a city are grouped into 30 school districts, with each school district containing four schools. Suppose that a simple one-stage cluster sample of three school districts is taken for purposes of estimating the number of school children in the city who are
If one wished to sample this entire book for misspelled words according to a three-stage cluster sampling design, what could serve as primary sampling units, as secondary sampling units, as listing units, and as elementary units?
If one wished to sample this page for misspelled words, what would be a logical cluster?
Given a sample of 100 elements, which of the following designs is likely to yield estimates having the highest standard errors?a. Systematic samplingb. Cluster sampling Simple random samplingd. Stratified random sampling
For the illustrative example in Section 7.3, suppose that the known number of hospitals in subdomain 1 is 50, and in subdomain 2 is 51.a. Determine the poststratified ratio estimate of the proportion of newborns discharged with the mother's hepatitis В surface antigen status documented on the
A large plant has 1000 workers. A simple random sample of 25 workers is taken to find the ratio of work-loss days to total days employed during the previous calendar year. The following data were obtained from the survey:Total work-loss days among the 25 individuals sampled: 250 Total days employed
The following exercise was suggested by an article appearing in Public Health Reports [3|. A survey was taken to determine the incidence of HIV seroconversion among first-time blood donors at a blood center located in a large city. During a particular month, 180 first-time donors gave blood at the
Show that, for simple random sampling, the correlation p^, between estimated totals x' and y' of characteristics К and ^P is equal to p the correlation between X and y.
A sample survey is to be conducted in which it is desired to estimate the proportion of persons over 70 years of age who have evidence of a cognitive impairment. This is to be done by taking a sample of households and giving a simple test of cognitive functioning to all members of the household
Based on the data in Exercise 7.5, how many patients would have to be sampled if a ratio estimate were to be used?
Based on the data in Exercise 7.5, how many patients would have to be sampled if a simple inflation estimate were to be used?
It is desired to estimate the total X of nurse practitioner hours spent in direct patient care in a large HMO during a given year. This is to be done by taking a simple random sample of patients and determining, for each visit during the year, the number of nurse practitioner hours spent during the
For the data in the table accompanying Exercise 7.2, obtain a regression estimate of the total weekly medical expenditures paid by the community. Give 95% confidence intervals for the true value of this parameter based on this regression estimate.
For the city cited in Exercise 7.2, it is also desired to estimate, with virtual certainty, the total moneys spent on medical expenses to within 10% of its true value. How many families would have to be sampled if these specifications were to be met?
The table on the facing page, based on a simple random sample of 33 families from a community of 600 families, gives the family size, weekly net family income, and weekly cost of medical expenditures including pharmaceuticals.The community contains 2700 persons.a. Estimate, and give a 95%
A sample survey is being planned in which it is desired to estimate the average ratio of medical expenses to family income in a large city containing 234,785 families. Based on data in the table accompanying Exercise 7.2, how many families would have to be sampled if it is desired to estimate with
This exercise relates to the illustrative example on screening for twins discussed in Section 6.5. White female-female pairs were constructed as described in the illustrative example on the basis of same date of birth and SS#'s matching on the first seven digits. The number of pairs so constructed
A marathon was conducted in a large city on September 3, 1989. Based on the entry applications, the following data were obtained.Age Group£30 30-49 50+N 2300 1478 978 Mean Number of Marathons Completed ( X )1.9 2.3 3.1 Standard Deviation σχ.6.8.7 It is desired to take a sample of approximately
In a large population survey, 15,000 persons were screened with chest radiographs. Physicians noted possible pulmonary artery enlargement in 230 of these patients. This enlargement was confirmed by a second reading in 203 of these 230 persons. A sample of 175 of the 14,770 chest radiographs in
Esther (the same Esther from Exercises 6.6 and 6.7) feels that it would only be worthwhile to do her survey if she can be 95% certain of estimating the rate to within 15% of its true value. She anticipates that the true overall rate will be about 12%. Based on her funding level indicated in
Esther (the heroine of Exercise 6.6) obtains $25,000 from BBAAS (Body Builders Against Anabolic Steroids) to conduct her survey. This will be her only source of funding. She estimates that it would cost $30.00 per interview in strata 1 and 2 and $40.00 per interview in stratum 3. With this in mind,
Esther is an epidemiologist and a very successful amateur body builder ("Ms.Drug Free Chicago Upper Body, 2000"). She is planning a survey of Chicago-area body builders to determine the proportion who have ever used anabolic steroids. Her sampling frame consists of membership lists obtained from
A marketing research firm specializing in the health-care industry has a file containing approximately 150,000,000 names organized by ZIP codes (the file contains 65,000 ZIP codes). A stratified random sample is to be taken with ZIP codes as the strata and proportional allocation. The purpose of
Consider the 40 workers presented in Table 3.8 to be a simple random sample from the 1200 workers in the plant.a. Compute a 90% confidence interval for the population mean forced vital capacity.b. Suppose it is known, prior to analyzing the data, that the 1200 workers were distributed as
Let us suppose that a household survey is to be taken for the purpose of estimating characteristics of families having female household heads. Since it is not known in advance of the survey which families have female household heads, the sample households will be screened and those sample
Let us suppose that the data from Table 3.8 were obtained from a stratified random sample of the 1200 workers in the plant in which the workforce was stratified according to pulmonary Stressors (high, medium, low) and that proportional allocation was used to allocate the sample.a. How many workers
A sample survey of households in a community containing 1500 households is to be conducted for the purpose of determining the total number of persons over 18 years of age in the community who have one or more permanent teeth(other than third molars) missing. Since this variable is thought to be
A simple random sample (without stratification) of 30 of these 56 patients yielded the following data:Number of Persons CD4 Level Number of Events 01 23 Estimate the incidence of AIDS-defining events from these data and the standard error of this estimate. Compare this with the results obtained
From the data in Exercise 5.8, estimate the proportion of patients having one or more AIDS-defining events. What is the standard error of this estimated proportion?
The results of the sample survey described in Exercise 5.7 are shown below:Number of Persons CD4 Level 0From these data, estimate the incidence of AIDs defining events in the target population. What is the standard error of the estimated incidence rate?
In a large clinic located in an inner city hospital, 56 patients with nonsymptomatic 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
Suppose that in the situation given in Exercise 5.5, it is desired to estimate the number of encounters per physician in 2008. Repeat parts (a)-(d) in Exercise 5.5 for this estimation situation. Is stratified random sampling superior to simple random sampling in this situation? Why is it or why is
The following data are available for 2007 for six health maintenance organizations (HMOs) in a medium-size city:Number of personnel providing patient care and number of patient encounters during 2007 among six HMOs No. of Physicians Providing No. of HMO Patient Care Patient Encounters 1 10 22,000 2
An additional 2000 runners entered the race but did not complete it. Of these runners, a mail questionnaire was sent to a random sample of 600 and completed by 500. One of the items in this questionnaire asked the respondent to estimate the average number of miles run weekly during the 8 weeks
If a stratified random sample of 333 persons in each of the three groups had been taken, what would likely be the resulting estimated percentage positive?
Suppose that in the situation of Exercise 5.1, of the 10,000 completing the marathon, 2000 completed the event in less than 2.5 h, 6000 completed the event in 2.5-4.0 h, and 2000 completed the event in more than 4 h. Comment on the results of the sampling as given in Exercise 5.1.
From a simple random serological sample of 1000 runners selected from 10,000 who completed the 2007 Chicago Marathon, 35 were found to be positive for steroids and other performance-enhancing drugs. When categorized by completion time, the results were as follows:Completion Time (h)Under 2.5
The sample described in Exercise 4.12 yields the following data on the 100 HMO enrollees selected as described above. From these data, estimate the proportion of persons in the HMO population at high risk for coronary heart disease. Number of Record Records per CHD High Record Number of Records per
A data file contains 100,000 records on 2012 members of a health maintenance organization (HMO). Records are labeled beginning with "1 " and ending with "100,000," and a random number is selected between 1 and 1000.The random number selected is 253, and all records ending with 253 are sampled
Suppose that in the scenario of Exercise 4.1, it is decided to take a sample of 18 homes according to a repeated systematic sampling design that specifies 6 replications of a systematic sample of 3 homes.a. In the notation developed in this chapter for repeated systematic j sampling, specify N, M,
Systematic sampling works best under which of the following scenarios?a. The sampling frame (or list) is ordered with respect to a variable that is directly related to and highly correlated with the variable of interest.b. The sampling frame is neither ordered nor has any periodicity with respect
Which of the following is not true about systematic sampling?a. Variances of estimates are large when the sampling ratio coincides with a periodicity in the frame.b. Variances of estimates are related to the size of the intraclass correlation coefficient.c. Unlike simple random sampling, one does
During a 52-vveek period, there are 1820 (35x52) appointment slots in the situation described in Exercise 4.7. A repeated systematic sampling design of 1 in 26 appointment slots is to be used to estimate the proportion of appointments devoted to comprehensive care during that 52-vveek period. A
The following represents a week of scheduled appointments for the staff dentist at a small community health center characterized by major activity(B = Basic Care; С = Comprehensive Care) :Weekl It is desired to estimate the proportion of visits devoted to comprehensive care during a particular
During a specific year, 200 cardiac catheterization procedures were performed on persons over 70 years of age at a large university hospital. From the list of these patients, 4 systematic samples of 1 in 50 patients yielded the data on the next page relating to pulmonary artery pressure.Based on
Suppose that a study is planned of the level of the pesticide dieldrin, which is believed to be a carcinogen, in a 7.5-mile stretch of a particular river. To assure representativeness, a map of the river is divided into 36 zones (see the following figure) and a one-in-four systematic sample of
From the list of 162 workers in Table 4.17, use repeated systematic sampling to take a total sample of 18 workers for purposes of estimating the total number of work days lost due to acute illnesses by all workers and the proportion of workers having eight or more work days lost due to acute
Refer again to Exercise 4.1. Suppose that instead of a one-in-five systematic sample, a total of 24 sample homes are obtained by repeated systematic sampling of 1 in 40 homes.a. Suppose that the random numbers chosen are 3, 7, 12, 26, 31, 33, 38, and 40. Estimate the proportion of homes with lead
From the 120 homes of Exercise 1, suppose a one-in-five systematic sample was taken and suppose that the initial random number was 5.a. Estimate the proportion of homes with lead hazards from this sample.b. Obtain a 95% confidence interval for the proportion of homes with lead hazards.What is the
Suppose the local Childhood Lead Poisoning Prevention Council in a metropolitan area in western Tennessee undertakes the responsibility of determining the proportion of homes in a certain development of 120 homes with unsafe lead levels. Because of the great expense involved in performing
In the previous exercise, what is the employee's chance of being detected if he/she is "under the influence" on the job only 10% of the time?
A company containing 700 employees is planning to test employees for working under the influence of illicit drugs (e.g., cannabis and cocaine). During the course of a year, a sample of 3 days will be selected for testing, and on each of these days, a simple random sample of 50 employees will be
A city contains 20 neighborhood health clinics, and it is desired to take a sample of 5 of these clinics for purposes of estimating the total number of persons from all these clinics who had been given, during the past 12-month period, prescriptions for a recently approved antidepressant drug. If
In the previous example, if a simple random sample of the entire population is to be taken, how large a sample is required in order to be 95% certain of estimating within 10% of the true value, the proportion of the Asian population not covered by some form of health insurance (again assuming that
A community in the San Francisco Bay area consists of approximately 50,000 persons, of whom approximately 40% are Caucasians, 25% are African American, 20% are Hispanic, and 15% are Asian. It is desired to estimate in this community the proportion of persons who are not covered by some form of
A section of a random number table is reproduced here:a. Starting with the first random number in the upper left-hand corner of this table and reading down the columns, select a sample of 6 of the 25 physicians listed in Table 2.1.b. Estimate the mean number X of household visits made by physicians
A community within a city contains 3000 households and 10,000 persons. For purposes of planning a community satellite to the local health department, it is desired to estimate the total number of physician visits made during a calendar year by members of the community. For this information to be
A survey of workers is to be taken in a large plant that makes products similar to those made in the plant from which the data in Table 3.8 are obtained. The purposes of the survey are to estimate (a) the proportion of all workers having an fvc below 70% and (b) the mean fvc among all workers.
From the data in Table 3.8, estimate the proportion of workers in the plant having low or medium exposure to pulmonary Stressors. Give 95% confidence intervals for this estimated proportion.
From the data in Table 3.8 on the workers having low or medium exposure to pulmonary Stressors, estimate the proportion who have an fvc below 90% of that expected on the basis of age, sex and height. Give 95% confidence interval for this proportion.
How many simple random samples of 15 elements can be taken from a population containing 65 elements?3 3 From the data in Table 3.8, estimate the proportion of all workers in the plant having a fvc less than 70% of that expected on the basis of age, gender, and race. Give a 95% confidence interval
From the data in Table 2.1, using simple random sampling, take ten different samples of six physicians. For each sample, compute approximate 95% confidence intervals for the average number of household visits per physician. For how many of these calculated 95% confidence intervals is the true
Match the term in column 1 with the most appropriate term in column 2. Column 1 1. MSE 2. Reliability 3. Bias 4. Universe 5. Sample Total 6. Population Total Column 2 ... B. Population. C. Accuracy . . E. Validity F. Variance
The following table shows the total number of laboratory determinations for the 10 sample patients described in Exercise 2.6 as well as the number of invalid determinations among the 10 determinations sampled:
Data from the sample described in Exercise 2.6 are shown on the following page. Based on these data, what is the estimated proportion of laboratory results that are invalid?
It is desired to perform a quality control audit of laboratory data from a large clinical trial for purposes of estimating the proportion of laboratory values in the database that are invalid. There are 394 patients in the clinical trial, and each person has had from 60 to 200 laboratory
As part of a marketing program, a city block containing four households was selected and a sample of three households was sampled as follows: Jeremiah, the research assistant, identified the households and numbered each household from 1 to 4. He then was to list all combinations of the four
As part of an AIDS education program, 120 intravenous drug users seronegative for HIV (Human Immunodeficiency Virus) at a first screening were given instructions on sterilizing their needles with bleach and practicing "safe sex."One year after the program's inception, a sample of 30 of these
Suppose that a survey is being planned for purposes of estimating the average number of hours spent exercising daily by adults (18 years of age or older)living in a certain community. A list of all individuals living in the town is not available; however, a list of all households is available at
For each of the following problems, indicate how you would carry out a sample and specify these entities:a. The populationb. The variable(s)The elementary unitd. The framee. The enumeration unit 1. Suppose we wish to estimate the average cost of an appendectomy in a certain state. There are 27
You are the chief executive officer of a hospital and wish to know within a very short time the proportion covered by third-party carriers other than Medicare or Medicaid of all inpatient admissions within 2006. How would you go about determining this proportion?l j As the same CEO as in Exercise
Feedback from a pilot study will generally yield which of the following benefits?a. Lowering of measurement errors b . Lowering of sampling errorsc. Decrease in costsd. All of the above
Which of the following best describes estimates obtained from a census?a. Both sampling and measurement errors presentb. Sampling errors but not measurement errors presentc. Measurement errors but not sampling errors presentd. Neither sampling nor measurement errors present
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