MATH 350 - SURVEY SAMPLING

The objective of a sample survey is to make inferences about the population from information contained in a sample. Two factors affect the quantity of information contained in the sample. The first is the size of the sample. The second is the amount of variation in the data; variation can frequently be controlled by the method of selecting the sample (called the sample survey design). In this course, the four most common sample survey designs are introduced; they are simple random sampling, stratified random sampling, systematic sampling and cluster sampling. Ratio, regression, and difference estimation are also discussed. Practical aspects of conducting sample surveys, methods of data collection and designing questionnaires are considered as well. Two interesting problems that may be encountered in this course are given below.

CAN WE ESTIMATE THE TOTAL COST OF HEALTH CARE?

An important problem of national concern involves the estimation of the cost of health care. These costs are studied by both the government and private sectors in order to establish government policies and to assess business decisions such as the rates for insurance policies.

A method of estimating hospital costs for one disease is considered in the article "Economic Impact of Kidney Stones in White Adult Males" by Shuster and Sheaffer (Urology, vol. 24, no. 4, 1984). In this work, two regions of the United States, the Carolinas and the Rocky Mountain states, were singled out for special study. A sample of n1= 363 stone patients in the Carolinas had an average cost for first hospitalization of $1350; a sample of n2 = 258 stone patients in the Rockies had an average cost for fist hospitalization of $1150. Can we estimate the total annual hospitalization costs for this disease for both regions combined? The method of stratified random sampling will show us how to do so if some additional information is available. This method can then be used to find an estimate for the entire United States if sample information is available for other regions.

 

CAN WE ESTIMATE THE POPULATION SIZE OF BIRDS?

Authorities of a large wildlife preserve are interested in the total number of birds of a particular species that inhabit the preserve. A random sample of 50 birds of this species is trapped, tagged and then released. Two weeks later a second sample is drawn until 12 tagged birds are recaptured. In total, 35 birds of this species are recaptured in order to find 12 tagged ones. How do we estimate the population size of this particular species of birds? How do we place a bound on the error of estimation?

INTENDED AUDIENCE
Students interested in Mathematics and/or Statistics.
PREREQUISITES
MATH 106 with at least a B, or MATH 270, or MATH 104 with a B+
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