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Chapter 6

# Chapter 6 - Chapter 6 Using the Normal distribution for...

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Chapter 6: Using the Normal distribution for confidence intervals and hypothesis testing for a population mean NO SPSS in this chapter! Ellen Gundlach STAT 301 Course Coordinator Purdue University

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What can we do with our sample data? Statistical inference : hypothesis testing and confidence intervals Population Sample (parameter) (statistic) Inference Sampling
Confidence intervals allow us to estimate the population parameter

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Confidence interval created from our sample Population mean Where we sample

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“Confidence” The 95% confidence refers to our method and how well it works over the long run. Applet: http://bcs.whfreeman.com/scc6e/content/cat_040/spt/confidence/confidenceinterval.html Video of me using the applet: http://www.screencast.com/users/EllenGundlach/folders/Jing/media/82da5663-46d1-40d3-ba2a-ba3fb53dcbf2
Sample size As sample size , margin of error (width) .

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Confidence level As confidence level , margin of error (width) .
Is a bigger CI better? Confidence level Sample size

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Confidence interval formulas If you know the population standard deviation, σ: Confidence level 90% 95% 99% Z* 1.645 1.960 2.576 * x z n σ ±
Margin of error, sample size The margin of error: Know margin of error, want to know sample size: * m z n σ = 2 * z n m σ =

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Confidence interval example A questionnaire of drinking habits was given to a random sample of 30 fraternity members, and each student was asked to report the # of beers he had drunk in the past month. The sample resulted in an average of 22 beers with a population standard deviation of 9 beers. Give a 90% confidence interval for the population mean number of beers drunk by fraternity members in the past month.
Confidence interval example Give a 90% confidence interval for the population mean number of beers drunk by fraternity members in the past month. 22, 9, 30, 90%, * 1.645 9 * 22 (1.645) 22 2.7 30 (19.3, 24.7) x n C z x z n σ σ = = = = = ± = ± = ±

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Confidence interval example How many students should you sample if you want a margin of error of 1 for a 90% confidence interval?
Confidence interval example How many students should you sample if you want a margin of error of 1 for a 90% confidence interval?

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Chapter 6 - Chapter 6 Using the Normal distribution for...

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