33 - Chapter 8: Statistical Inference: Confidence Intervals...

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Chapter 8: Statistical Inference: Confidence Intervals Section 8.1 What are Point and Interval Estimates of Population Parameters?
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Learning Objectives 1. Point Estimate and Interval Estimate 2. Properties of Point Estimators 3. Confidence Intervals 4. Logic of Confidence Intervals 5. Margin of Error 6. Example
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Learning Objective 1: 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.
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Learning Objective 1: 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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Learning Objective 2: 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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Learning Objective 2: 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 The sample mean has a smaller standard error than the sample median when estimating the population mean of a normal distribution
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Learning Objective 3: 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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Learning Objective 4: Logic of Confidence Intervals To construct a confidence interval for a population proportion, start with the sampling distribution of a sample proportion Gives the possible values for the sample proportion and their probabilities Is approximately a normal distribution for large random samples by the CLT Has mean equal to the population proportion Has standard deviation called the standard error
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Fact: Approximately 95% of a normal distribution falls within 1.96 standard deviations of the mean With probability 0.95, the sample proportion falls within about 1.96 standard errors of the population proportion The distance of 1.96 standard errors is the margin of error in calculating a 95% confidence interval for the population proportion Learning Objective 4: Logic of Confidence Intervals
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5: Margin of Error The margin of error measures how accurate the point estimate is likely to be in estimating a parameter It is a multiple of the standard error of the sampling distribution of the estimate when the sampling distribution is a normal distribution. The distance of 1.96 standard errors in the
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33 - Chapter 8: Statistical Inference: Confidence Intervals...

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