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Unformatted text preview: 1 Sampling and Sampling Distributions Simple Random Sampling Point Estimation Introduction to Sampling Distributions Sampling Distribution of Sampling Distribution of Properties of Point Estimators x p 2 Statistical Inference The purpose of statistical inference is to obtain information about a population from information contained in a sample. A population is the set of all the elements of interest in a study. A sample is a of the population. A parameter is a numeric measure of a population. For instance, the probability p of a success in a binomial experiment. A sample statistics is a numeric measure of a sample, such as the sample mean and sample variance. subset 3 Point Estimation In point estimation we use the data from the sample to compute a value of the sample statistic that serves as an of a population parameter. We refer to as the of the population mean . s is the point estimator of the population standard deviation . is the point estimator of the population proportion p . x p estimate point estimate 4 Parameter Point Estimator Population Sample p p Prop. s Std. x Mean 5 Example: St. Edwards St. Edwards University receives 7,000 applications annually from prospective students. The application forms contain a variety of information including the individuals scholastic aptitude test (SAT) score and whether or not the individual is an instate resident. The director of admissions would like to know, at least roughly, the following information: the average SAT score for the applicants, and the proportion of applicants that are instate residents. We will now look at two alternatives for obtaining the desired information. 6 Alternative #1: Take a Census of 7,000 Applicants (Results are calculated from the data not shown completely.) SAT Scores Population Mean Population Standard Deviation InState Applicants Population Proportion 7 0 0 0 1 9 9 0 7 , 0 0 0 i i x 7000 2 1 ( ) 80 7, 000 i i x 72 . 000 , 7 040 , 5 p Example: St. Edwards 7 Take a random sample of 50 applicants. No. Applicant SAT Score InState 1 Bonnie Reight 1025 Yes 2 Willie Neilson 950 Yes 3 Fannie Lennox 1090 No 4 Derek Clapton 1120 Yes 5 Winona Driver 1015 Yes . . . . . . . . 50 Kevin Costmore 965 No Total 49,850 34 Yes Example: St. Edwards 8 Point Estimates (Results are calculated from the data not shown completely.) as Point Estimator of s as Point Estimator of as Point Estimator of p Note: Different set of random numbers would have identified a different sample which would have resulted in point estimates....
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This note was uploaded on 09/28/2011 for the course STAT METHO 33:623:385 taught by Professor Faridalizadeh during the Spring '11 term at Rutgers.
 Spring '11
 FaridAlizadeh

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