Week 4 CI and Hypothesis Testing

Week 4 CI and Hypothesis Testing - Engr 9397 – Week 4...

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Unformatted text preview: Engr 9397 – Week 4 Sampling, Distributions, Confidence Limits and Hypothesis Testing Sampling and Sampling Distributions • Sampling allows us to assess the accuracy of our estimates of population distribution parameters • To ensure that a sample is representative of the population, the set of recorded observations that constitutes the sample must be random • In terms of probability distributions: – Each observation of n is a value of a random variable having a distribution f(x) – The n random variables are independent from each other Drawing Inferences from samples • Combining our knowledge of probability and sampling, we can use sample data to draw inferences about underlying populations • A statistic is some quantity computed from the data (ex. mean, std dev, etc.) • Point Estimators are statistics computed from a random sample that are used to estimate population distribution parameters (ex. sample mean) Statistical Inference • Statistical inference: theories and methods for making statements about population parameters based on random samples – Estimation: uses sample result to find a point estimate or a confidence interval of a population parameter (population parameters include , , etc.) – Hypothesis testing uses sample results to test the validity of initial statements made about population parameters (also called a significance test) Sampling Distributions • The sampling distribution allows us to assess the accuracy of estimates of population distribution parameters (statistics) and to formulate an approach to hypothesis testing • We cannot determine exactly how close our estimate is to the true value of the population parameter, but we can determine in general, how close the estimate is to the true value • We can assess the accuracy of our estimates by considering what might be true if we have many sets of samples of the same size Sampling Distribution continued • We are interested in determining the accuracy of a statistic, t of some population distribution parameter of interest, which we’ll symbolize as X • Let x 1 , x 2 , etc. represent the values of random sample distributions of size n taken from the population • We compute t 1 , t 2 , etc. to be the corresponding sample estimates of the true value of the population parameter of interest • Our inference statements indicate with what chance that a given t will fall within a particular range that will include the true value of the population parameter Sample Bias • Sample statistics inherently contain error • Recall: error consists of bias (lack of accuracy) and random error (lack of precision) • Bias in a sample occurs when the mean of a given sample distribution is different from the mean of population parameter being estimated • Bias = lack of accuracy, repeated estimates have values consistently different than the parameter to be estimated • Here the parameter we are interested in is , the sample mean Sample Variability...
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This note was uploaded on 03/29/2011 for the course ENGR 9397 taught by Professor Susanhunt during the Winter '11 term at Memorial University.

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Week 4 CI and Hypothesis Testing - Engr 9397 – Week 4...

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