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## Practice

by: Samantha Notetaker

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# Practice

Samantha Notetaker
Mercer

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This 2 page Class Notes was uploaded by Samantha Notetaker on Monday August 1, 2016. The Class Notes belongs to at Mercer University taught by in Fall 2016. Since its upload, it has received 4 views.

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Date Created: 08/01/16
Math 2400: Statistics  MWF 11:00­11:50 Dr. Brad Bailey April 11th, 2016 Confidence Intervals (Theory and Practice) Recall the Law of Large Numbers and the Central Limit Theorem  ­ The Law of Large Numbers: is xx is a sample average of size “n” taken from a population  with (probably unknown) means of  μ,then as “n” approaches infinity, xx approachesμ. ­ The Central Limit Theorem: Even if the original population is not normal, as "n”  σ √n¿ σ increases, the sampling distribution will approach N(μ ,  / , where   is  the population.  ­ About 95% of any normal distribution will fall within two standard deviations of the  mean. (For improved accuracy, we often use 1.96 instead of 2) σ √n σ √n ­ Starting from μ ­ 1.96(  / ) and ending atμ + 1.96(  / ), we capture  95% of all possible xxs.  ­ For a given xx, there is a 95% chance it is with in 1.96(  / √n ) ofμ.  ­ So … xx + 1.96(  σ / √n ) is a 95% confidence interval.  σ √n ­ / : Standard Error ­ Confidence Interval: an interval that you’re 95% sure contains the real mean.  Calculator: ­ If calculating the confidence interval from a t­test, use a t­interval; if calculating the  confidence interval from a z­test, use a z­interval. ­ Instead of leaving the answer in the (524.62, 541.38) context, answer as xx    the  margin of error.  ­ So if xx= 533, answer like (541.38­533)= 8.33 … so 533 ± 8.38. ­ Or, the end/beginning interval­ xx= the margin of error  σ Use Z­Test: if you’re given a population standard deviation ( ) Use T­Test: S or Sx is a sample standard deviation  “Curving” or fitting to a bell curve: First order test scores from least to greatest Find their percentile Then go to the normal curve that has mean and standard deviation the professor wants.

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