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This 3 page Class Notes was uploaded by Debra Tee on Thursday October 13, 2016. The Class Notes belongs to STATS 250 at University of Michigan taught by Thomas Venable Jr in Fall. Since its upload, it has received 3 views. For similar materials see /class/231658/stats-250-university-of-michigan in Statistics at University of Michigan.
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Date Created: 10/13/16
Lecture 9: Estimating Proportions with Confidence 10.1: Overview of Confidence Intervals Confidence Intervals concept: Use sample data to estimate a population parameter Population (size N) = the whole group that we want to make conclusions on Parameter = summary about population Random sample of size n = a few units selected from population Statistic = summary about the sample Sample estimate = provides our best guess as to what is the value of the population parameter, but it is not 100% accurate. Concept: The value of the sample estimate will vary from one sample to the next. The values often vary around the population parameter and the standard deviation give an idea about how far the sample estimates tend to be from the true population proportion on average. The standard error of the sample estimate provides an idea of how far away it would tend to vary from the parameter value (on average). The general format for a confidence interval estimate is given by: Sample estimate ± (a few) standard errors 10.2: Confidence Interval for a Population Proportion p Probability that sample proportion ???? will be within 2 standard deviations from the true proportion p = 95%. Common mistake: Can we say that 95% of the time the population prop ortion p will be in the confidence interval for ????? NO, either p is in the particular interval or it is not! Interpreting the Confidence Level: Definition of 95% Confidence Level: If the sampling procedure were repeated many times, then approximately 95% of the resulting confidence intervals would contain the population proportion of xxx… Important concept: When Confidence level increases, width of confidence interval increases. Example: 90% Confidence Interval would be narrower than 95% Confidence Interval.
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