# Chapter 7 - Chapter 7: Confidence intervals and hypothesis...

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Chapter 7: Confidence intervals and hypothesis testing for 1-sample mean, matched pairs, and 2-sample comparison of means using the t distribution Ellen Gundlach STAT 301 Course Coordinator Purdue University

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Z (Normal distribution) Chapter 6 Population standard deviation, σ Unusual in real-life σ t Chapter 7 Sample standard deviation, s Real-life situation s
1-sample mean with the t distribution Confidence interval Test statistic Degrees of freedom = n - 1 * s x t n ± 0 / x t s n μ - =

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Using the t table and SPSS Need to know how to use t table and SPSS. If your degrees of freedom are not on t table (like df = 79), always round down to the next degree of freedom that is there. t table in the back of your book and here: http://www.stat.purdue.edu/~gundlach/stat301/index_files/Page612.htm

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One-sample mean CI and HT t table approach An agricultural expert performs a study to measure yield of a tomato field. Studying 10 plots of land, she finds the mean yield is 34 bushels with a sample standard deviation of 12.75 bushels. Find a 95% confidence interval for the population mean yield of tomatoes.
One-sample mean CI and HT t table approach 34, 10, 12.75, 95% With n=10, degrees of freedom will be 9. t* will be 2.262. 12.75 * 34 2.262 10 34 9.12 (24.88, 43.12) x n s C s x t n = = = = ± = ± ± =

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One-sample mean CI and HT t table approach An agricultural expert performs a study to measure yield of a tomato field. Studying 10 plots of land, she finds the mean yield is 34 bushels with a sample standard deviation of 12.75 bushels. Conduct a hypothesis test with α = 0.05 to determine if the population mean yield of tomatoes is less than 42 bushels.

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One-sample mean CI and HT t table approach 0 0 0 34, 10, 12.75, 42 With n=10, degrees of freedom will be 9. : 42 : 42 34 42 1.98 / 12.75/ 10 -value ( 1.98) ( 1.98) 0.025 -v a x n s H H x t s n P P t P t P μ = = = = = < - - = = =- = <- = 0 alue 0.05 Since P-value is , reject H . We have evidence the population mean yield of tomatoes is less than 42 bushels. α
Using the t table to get a P-value

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One-sample mean CI and HT t table approach 0 0 34, 10, 12.75, 42 : 42 : 42 1.98 -value ( 1.98) ( 1.98) 0.025 -value 0.05 a x n s H H t P P t P t P μ = = = = = < = - = < - = +
1-sample mean test and CI by hand and with SPSS How accurate are radon detectors of a type sold to homeowners? To answer this question, university researchers placed 12 detectors in a chamber that exposed them to 105 picocuries per liter of radon. The detector readings were as follows: 91.9 97.8 111.4 122.3 105.4 95.0 103.8 99.6 119.3 104.8 101.7 96.6

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1-sample mean test and CI by hand and with SPSS
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## This note was uploaded on 11/08/2010 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Chapter 7 - Chapter 7: Confidence intervals and hypothesis...

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