Intro Stats Week 9

No matter what population the random sample comes

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Unformatted text preview: s a sample distribution with the same mean mu but whose standard deviation is sigma/rad(n). No matter what population the random sample comes from, the shape of the sampling distribution is Normal as long as the sample size is large enough. Confidence Intervals for Proportions 51.9% of all sea fans on the Las Redas Reef are infected It is probably true that 51.9% of all sea fans on the Las Redas Reef are infected We don’t know exactly what proportions of sea fans on the Reef are infected, but we know that it’s within the interval 51.9% +/4.9%. That is, between 42.1% and 61.7%. 3 10/30/2011 Technically ◦ We don’t know exactly what proportion of sea fans on the Reef is infected, but the interval from 42.1% to 61.7% probably contains the true proportion We We are 95% confident that between 42.1% and 61.7% of Las Redas sea fans are infected ◦ Now that’s a confidence interval! ◦ The interval calculated and interpreted here is sometimes called a one-proportion z-interval onez- Confidence interval: Confidence interval p-hat +/- 2 SE(p-hat) The extent of the interval on either side of phat is called the margin of error (ME) ◦ Use the same approach for all other situations ◦ Not just proportions! ◦ General format: Estimate +/- ME +/- Formally, 95% of samples this size will produce confidence intervals that capture the true proportion We are 95% confident that the true proportion lies in our interval Our uncertainty is about whether the particular sample we have at hand is one of the successful ones of one of the 5% that fail to produce an interval that captures the true value Independence Independence Assumption ◦ Randomization Condition: Were the data sampled at random or generated from a properly randomized experiment? ◦ 10% Condition: If the sample exceeds 10% of the population, the probability of a success changes so much during sampling that Normal model might not be appropriate The more confident we want to be, the larger the margin of error will be! Tension between certainty and precision Sample Sample Size Ass...
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This document was uploaded on 02/11/2014.

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