Unit 8-1

Unit 8-1 - Confidence Intervals Rate your confidence Rate 0...

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Confidence Intervals

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Rate your confidence Rate your confidence 0 - 100 0 - 100 Name my 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 larger your confidence, the wider the interval.

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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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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.
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%

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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
Activity Activity

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Steps for doing a confidence Steps for doing a confidence interval: interval: 1) Assumptions – SRS from population Sampling distribution is normal (or approximately
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This note was uploaded on 12/09/2011 for the course STATS 221 taught by Professor Nielson during the Fall '10 term at BYU.

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Unit 8-1 - Confidence Intervals Rate your confidence Rate 0...

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