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Unformatted text preview: 1 Ch 8 Notes-AG-B 3/15/2010 Chapter 8 Statistical Inference: Confidence Intervals First, reviewing what we have learned: Statistics is a way of dealing with the uncertainty of how our world works Decision making with imperfect data Based on our perceptions which have been influenced by prior learning, both formal (schooling) and informal (our own experimentations) Statistics works with theoretical models We form a hypothesis and then we test it to determine if our model is right We test the underlying conditions and assumptions about the model first to make sure we can use it. Ex. Binomial has only two outcomes, etc. Sampling error cannot be eliminated if we are working with samples. We look for patterns in data when attempting to develop the theoretical model Descriptive statistics: organization, summarization and display of data in order to make sense of it Inferential statistics: sample used to draw conclusions about a population uses probability to help determine likelihood of something happening Used to clarify or prove a current hypothesis Confidence Intervals We construct a interval around a point estimate with some confidence that the interval contains the population parameter. Population parameters are unknown while sampling parameters are known. We are trying to use the known to estimate what the unknown is. We cant be sure we are right but we can have a certain confidence about it. The larger the better is the rule of thumb for samples when using them to estimate the population proportion. Assumptions about the population are based on randomized experiments or a random sample. We use the CLT which says that the sampling distribution of a statistic is usually a normal distribution. Sample size depends on the level of accuracy needed not the size of the population. Needed level of accuracy based on: o Safety issues will someone be hurt if you are wrong? o Cost issues what will it cost you or your company if you are wrong? 2 Ch 8 Notes-AG-B 3/15/2010 Point and Interval Estimates of Population Parameters Point Estimate and Interval Estimate # A point estimate is a single number that is our best guess for the parameter # An interval estimate is an interval of numbers within which the parameter value is believed to fall. # A point estimate doesnt tell us how close the estimate is likely to be to the parameter # An interval estimate is more useful o It incorporates a margin of error which helps us to gauge the accuracy of the point estimate Properties of Point Estimators # Property 1: A good estimator has a sampling distribution that is centered at the parameter o An estimator with this property is unbiased The sample mean is an unbiased estimator of the population mean The sample proportion is an unbiased estimator of the population proportion # Property 2: A good estimator has a small standard error compared to other estimators o This means it tends to fall closer than other estimates to the parameter...
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