L4 Populations, Samples and Estimation

# L4 Populations, Samples and Estimation - Populations...

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Populations, Samples and Estimation. Consider 3 quite different scenarios. 1) A manufacturer of electronic fuses needs to know the maximum amps at which a any one of a batch of fuses will burn out. Testing every one to destruction will leave none to sell, so a few of them are examined to get an idea of the properties of the batch as a whole. 2) The government of a large country needs to know what proportion of the population will be eligible for benefits in a health program directed at preventing a particular disease. It is not possible to examine everyone in the country for susceptibility to the disease (some of whom will have died and others who will have born during the examination process) so a much smaller group of individuals is examined in order to gage the likely proportion in the population that are susceptible. 3) A local authority, responsible for providing an emergency response team for car crash victims on a collection of highways, needs to know the likely monthly frequency and location of crashes in order to establish the size of, and resources for, the response team. The location and number of crashes per month in recent history is used as a guess of what the likely locations and frequencies would be. Each of these three cases has all the characteristics of the problem facing a statistician, the need to glean some information about an always obscure and often large collection of things - the Population of Interest - by examining a much smaller and very real sub group of that collection - The Sample. When every element in the population is identified and the relevant characteristic recorded, the resultant data set is referred to as A Census; it constitutes a complete record of The Population of Interest. It is not necessarily an infinite list (the complete batch of fuses could certainly all be examined, the population of a country could certainly all be counted at a point in time) though sometimes it is (the number of places that accidents could take place in a highway system is infinite and the theoretical frequency with which they occur on average over a given period of time is certainly obscure and unobservable). When for various reasons (economic, feasibility, or practical) a census cannot be taken, the Population of Interest is something about which we can only conjecture. Typically in statistics the characteristic of the population we are interested in is treated as a random variable and a probability density function (p.d.f.) is used to describe its

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distribution across the range of potential values. One of the arts of practising applied statistics is that of choosing the right distribution for the problem at hand and estimating the parameters upon which the distribution depends.
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## This note was uploaded on 03/23/2011 for the course ECONOMICS 209 taught by Professor Kambourov during the Spring '11 term at University of Toronto.

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L4 Populations, Samples and Estimation - Populations...

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