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Chapter8_1

# Chapter8_1 - Sampling Distributions Chapter 8 Confidence...

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Chapter 8: Confidence Intervals Read Chapters 8 and 9 Sampling Distributions A sample statistic is a random variable ! This means that it has its own distribution. Def 1: The probability distribution of a sample statistic is called the sampling distribution of that statistic. Def 2: The sampling distribution of a statistic is the population of all possible values for that statistic under repeated sampling with a fixed sample size. 3 If random samples, each consisting of n measurements, are repeatedly drawn from the same population having true mean μ and standard deviation σ , then when n is large, the relative frequency histogram for the sample means (calculated from the repeated samples) will be approximately normal with mean and standard deviation , that is, Central Limit Theorem ~ approx Normal( , ) X n n 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. 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 ² 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 ² 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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Properties of Point Estimators ± Property 2: A good estimator has a small standard error compared to other estimators ² This means it tends to fall closer than other estimates to the parameter ± The sample mean has a smaller standard error than the sample median when estimating the population mean of a normal distribution 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 (1- α )x100% ² This is a number chosen to be close to 1,
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Chapter8_1 - Sampling Distributions Chapter 8 Confidence...

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