Confidence Intervals-2009

# Confidence Intervals-2009 - Confidence Intervals Chapter...

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Confidence Intervals Chapter 10.1

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Rate your confidence Rate your confidence 0 - 100 0 - 100 Guess Mrs. Pugh’s age within 10 years? within 5 years? within 1 year? Shooting a basketball at a wading pool, will make basket? Shooting the ball at a large trash can, will make basket? Shooting the ball at a carnival, will make basket?
What happens to your confidence as the interval gets smaller? The smaller the interval, the lower your confidence. % % % % % % %

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Point Estimate Use a single single statistic based on sample data to estimate a population parameter Simplest approach But not always very precise due to variation variation in the sampling distribution
Confidence intervals Confidence intervals Are used to estimate the unknown population mean Formula: estimate + margin of error

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Margin of error Margin of error Shows how accurate we believe our estimate is The smaller the margin of error, the more precise more precise our estimate of the true parameter Formula: = statistic the of deviation standard value critical m
Confidence level Confidence level Is the success rate of the method used to construct the interval Using this method, ____% of the time the intervals constructed will contain the true population parameter

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Found from the confidence level The upper z-score with probability p lying to its right under the standard normal curve Confidence level tail area z* .05 1.645 .025 1.96 .005 2.576 Critical value (z*) Critical value (z*) .05 z*=1.645 .025 z*=1.96 .005 z*=2.576 90% 95% 99%
Confidence interval for a Confidence interval for a population mean: population mean: ± n z x σ * estimate Critical value Standard deviation of the statistic Margin of error

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What does it mean to be 95% What does it mean to be 95% confident? confident? 95% chance that μ is contained in the confidence interval The probability that the interval contains μ is 95% The method used to construct the interval will produce intervals that contain μ 95% of the time.
A level C confidence interval for a parameter has two parts: An interval calculated from the data, usually of the form A confidence level C, which gives the probability that the interval will capture the true parameter value in repeated samples.

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