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Confidenceinterval

# Confidenceinterval - Sampling and Sampling Distributions...

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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

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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

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4 Parameter Point Estimator Population Sample p p Prop. s σ Std. x μ Mean
5 Example: St. Edward’s St. Edward’s University receives 7,000 applications annually from prospective students. The application forms contain a variety of information including the individual’s scholastic aptitude test (SAT) score and whether or not the individual is an in-state 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 in-state residents. We will now look at two alternatives for obtaining the desired information.

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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 In-State Applicants Population Proportion 7000 1 990 7,000 i i x 7000 2 1 ( ) 80 7,000 i i x 72 . 000 , 7 040 , 5 p Example: St. Edward’s
7 Take a random sample of 50 applicants. No. Applicant SAT Score In-State 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. Edward’s

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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. x p 997 50 850 , 49 50 x x i 2 ( ) 277,097 75.2 49 49 i x x s 68 . 50 34 p Example: St. Edward’s different
9 Process of Statistical Inference The value of is used to make inferences about the value of .

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