Chapter 21B

# Chapter 21B - Understanding Confidence Intervals The...

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Understanding Confidence Intervals The General Form

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Outline Understanding Confidence Intervals Confidence Intervals for a Mean Different Level Confidence Intervals
Definitions The point estimate of a population parameter is the single value of the sample statistic used to estimate the parameter The 95% Margin of Error (95% M.O.E.) is the value that is added and subtracted to the point estimate to get an interval estimate for the population parameter

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Population Proportion Confidence Interval Point estimator Standard Deviation of Point Estimator 95% Margin of Error n p p p ) ˆ 1 ( ˆ 2 ˆ - ±
Estimating Any Population Parameter To estimate any population parameter with a sample statistic, we can still use the 2 standard deviation rule to get the 95% Margin of Error. But the 2 standard deviation rule only applies to the Normally distributed variables. Are all sample statistics (point estimators) Normally distributed?

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Examples of Normally Distributed Sample Statistics (Well Quasi) 1000 different samples of size 30 were taken. Get the value of the sample statistic for each sample of 30. Make a histogram of all results. Do all of the sample statistics look Normally Distributed? Frequency 172.5 170.0 167.5 165.0 162.5 160.0 157.5 80 60 40 20 0 224 216 208 200 192 184 176 120 90 60 30 0 96 88 80 72 64 56 48 40 80 60 40 20 0 176 172 168 164 160 156 152 120 90 60 30 0 Mean Maximum Range Median Different Statistics Computed On Samples of Size 30
Central Limit Theorem Nearly any statistic computed on a sample is normally distributed if the sample size is large enough.

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Result To estimate a population parameter with 95% confidence point estimate ± 95% Margin of Error
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