Aem 201 1st Edition Lecture 14Outline of Last LectureI. Sampling DistributionII. Methods of Sampling-Probability Sampling TechniquesIII. Nonprobability Sampling TechniquesIV. Point EstimationV. Desirable Characteristics of Point EstimatorsOutline of Current LectureI. Desirable Characteristics of Point EstimatorsII. Sampling DistributionsIII. The Sampling Distribution of the Sample MeanCurrent LectureDESIRABLE CHARACTERISTICS OF POINT ESTIMATORS- Efficiency: If two (or more) estimators produce unbiased estimates of the same parameter, the estimator with the smaller (smallest) standard error is said to have greater (greatest) efficiency- Consistency: the probability that the value of the point estimate falls within some given range about the parameter increases to 1 as sample size grows- Sampling Error: the difference between an unbiased point estimator and the actual value of the parameterSAMPLING DISTRIBUTION- Sampling Distribution: the probability distribution associated with a statistic- Standard Error: the standard deviation of a sampling distributionTHE SAMPLING DISTRIBUTION OF THE SAMPLE MEAN- The expected value of this distribution is - The standard deviation (also called the standard error) of this distribution is equal to:- As the sample size goes up the less variation is x bar- This rule is only true if the population is ‘infinite’ in a statistical senseo n/N is less than or equal to .05- The mean of all the sample means will equal the population mean- As the sample size gets bigger, the distribution becomes tighter- If we keep increasing the sample size, the mean will not change but the standard error will get smaller- Central Limit Theorem (for sample means): when selecting a simple random sample from a population, the sampling distribution of x bar can be approximated by a normal probability distribution as the sample size becomes large NO MATTER HOW THE ORIGINAL POPULATION IS DISTRIBUTEDo We can assume that any sample of at least n=30 is sufficient to assure that the central limit theorem will force the potential values of x bar to be normally distributed- If the original population is normal:o As the sample size increases, it does not become less normal. If the distribution of the population is normal, then so will the sampleo As sample size increases, bell curve gets taller- If the original population is not normal:o Extremes pinch off and starts to flatten out once the sample is sufficiently large (30)- We should be able to convert a question about x bar into a question about z- If the sample size is sufficiently large (n is greater than or equal to 30) then we can use the normal probability distribution to describe probabilities for potential values of the sampleo Even if the original distribution is not
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