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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
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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.
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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 μ μ 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
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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 μ μ = = = = = < = - = < - = +
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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 Is there convincing evidence that the mean reading of all detectors of this type differs from the true value of 105?
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