DMS 308; TOPIC 2; Statistical Estimation.ppt - Statistical...

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Monday, June 24, 2019DMS 3081Statistical Estimation
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Objectives of the lectureBy the end of this lecture, the student should be able to:1.Understand sampling distributions and central limit theorem 2.Undertake point estimation3.Undertake interval estimation4.Select a sample sizeMonday, June 24, 2019DMS 3082
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Sampling Distribution of the Sample MeansThe sampling distribution of the sample means is a probability distribution consisting of all possible sample means of a given sample size selected from a population, and the probability of occurrence associated with each sample mean. 8-7Monday, June 24, 20193DMS 308
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EXAMPLE 1The law firm of Hoya and Associates has five partners. At their weekly partners meeting each reported the number of hours they charged clients for their services last week.If two partners are selected randomly, how many different samples are possible?PartnerHoursDunn22Hardy26Kiers30Malinowski26Tillman228-8Monday, June 24, 20194DMS 308
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EXAMPLE 1…This is the combination of 5 objects taken 2 at a time. That is, 5252310c( !) /[( !)( !)]PartnersTotalMean1,248241,352261,448241,544222,356288-9Monday, June 24, 20195DMS 308
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EXAMPLE 1…Organize the sample means into a sampling distribution.8-10Monday, June 24, 20196DMS 308
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EXAMPLE 1… Compute the mean of the sample means and compare it with the population mean:The mean of the sample means = [(22)(1) + (24)(4) + (26)(3) + (28)(2)]/10=25.2The population mean = (22+26+30+26+22)/5 = 25.2Observe that the mean of the sample means is equal to the population mean.8-11Monday, June 24, 20197DMS 308
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Central Limit TheoremFor a population with a mean and a variance , the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed - with the mean of the sampling distribution equal to and the variance equal to - assuming that the sample size is sufficiently large.22/n8-12Monday, June 24, 20198DMS 308
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Point EstimatesA Point estimate is one value ( a point) that is used to estimate a population parameter.
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