notes509fall11sec44

notes509fall11sec44 - STAT 509 Sections 4.4,4.8 More...

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STAT 509 – Sections 4.4,4.8 – More Inference • We can do inference (CIs, hypothesis tests) about parameters other than a population mean. Confidence Interval for a Proportion • Suppose our data tell us only whether each observation has a certain characteristic. • We want to know how much of the population has that characteristic. • The proportion (always between 0 and 1) of individuals with a characteristic is the same as the probability of a random individual having the characteristic. Estimating proportion is equivalent to estimating the binomial probability p . Point estimate of p is the sample proportion : • Give every sampled individual a 1 (if it has the characteristic) or 0 (if it lacks it). Note n y p = ˆ is a type of sample average (of 0’s and 1’s), so CLT tells us that when sample size is large, sampling distribution of p ˆ is approximately normal.
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n : 100(1 – α )% CI for p is: How large does n need to be? Example 1: We wish to estimate the probability that a randomly selected part in a shipment will be defective. Take a random sample of 179 parts, and find 14
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notes509fall11sec44 - STAT 509 Sections 4.4,4.8 More...

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