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Lec_ch7 - Chapter 7 Statistical Inference Confidence...

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Agresti/Franklin Statistics, 1 of 87 Chapter 7 Statistical Inference: Confidence Intervals Learn …. How to Estimate a Population Parameter Using Sample Data
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Agresti/Franklin Statistics, 2 of 87 Section 7.1 What Are Point and Interval Estimates of Population Parameters?
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Agresti/Franklin Statistics, 3 of 87 Point Estimate A point estimate is a single number that is our “best guess” for the parameter
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Agresti/Franklin Statistics, 4 of 87 Interval Estimate An interval estimate is an interval of numbers within which the parameter value is believed to fall.
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Agresti/Franklin Statistics, 5 of 87 Point Estimate vs Interval Estimate
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Agresti/Franklin Statistics, 6 of 87 Point Estimate vs Interval Estimate A point estimate doesn’t tell us how close the estimate is likely to be to the parameter An interval estimate is more useful It incorporates a margin of error which helps us to gauge the accuracy of the point estimate
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Agresti/Franklin Statistics, 7 of 87 Point Estimation: How Do We Make a Best Guess for a Population Parameter? Use an appropriate sample statistic: For the population mean , use the sample mean For the population proportion , use the sample proportion
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Agresti/Franklin Statistics, 8 of 87 Point Estimation: How Do We Make a Best Guess for a Population Parameter? Point estimates are the most common form of inference reported by the mass media
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Agresti/Franklin Statistics, 9 of 87 Properties of Point Estimators Property 1: A good estimator has a sampling distribution that is centered at the parameter 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
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Agresti/Franklin Statistics, 10 of 87 Properties of Point Estimators Property 2: A good estimator has a small standard error compared to other estimators This means it tends to fall closer than other estimates to the parameter
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Agresti/Franklin Statistics, 11 of 87 Interval Estimation: Constructing an Interval that Contains the Parameter (We Hope!) Inference about a parameter should provide not only a point estimate but should also indicate its likely precision
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Agresti/Franklin Statistics, 12 of 87 Confidence Interval A confidence interval is an interval containing the most believable values for a parameter The probability that this method produces an interval that contains the parameter is called the confidence level This is a number chosen to be close to 1, most commonly 0.95
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Agresti/Franklin Statistics, 13 of 87 What is the Logic Behind Constructing a Confidence Interval? To construct a confidence interval for a population proportion, start with the sampling distribution of a sample proportion
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Agresti/Franklin Statistics, 14 of 87 The Sampling Distribution of the Sample Proportion Gives the possible values for the sample proportion and their probabilities Is approximately a normal distribution for large random samples Has a mean equal to the population proportion Has a standard deviation called the standard error
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