Estimation Point Estimates Industrial Engineering

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Presentation transcript:

Estimation Point Estimates Industrial Engineering

Overview Point versus interval estimates Estimators of a population mean Estimators of a population proportion Estimators of a population variance Estimating other parameters Method of Moments Maximum Likelihood Estimates

Statistics Descriptive Statistics is used to summarize a collection of data in a clear and understandable way. Ex: Histograms, box plots, stem and leaf plots. Inferential Statistics are used to draw inferences about a population from a sample. Ex: 10 subjects perform a task after 3 hours of training. They score 12 points higher than 10 subjects who perform the same task with no training. Is the difference real or could it be due to chance?

Point Estimators Suppose we have a new type of light bulb and we wish to test the bulbs for mean time to burn out.

Point Estimators We select 10 bulbs at random and test to burn out.

Point Estimators å = n i x X 1 10 1462 . 1483 1569 + = = 1,596.2

Point Estimators = X 1,596.2 Is called a point estimator of the true but unknown mean m.

Point Estimators Suppose we now select a new sample of ten bulbs.

Point Estimators X 10 1571 . 1567 1739 + = = 1,603.0

Point Estimators Different samples yield different point estimates of X 10 1571 . 1567 1739 + = = 1,603.0 Different samples yield different point estimates of the population mean.