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# Lecture20 - STAT 350 Lecture 19 & 20 8.2 Tests Concerning...

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STAT 350 Lecture 19 & 20 8.2 Tests Concerning Hypotheses About Means

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Welcome Back Homework #9 due Friday: Ch8: 4,6,12,15,16,19,20,22,26,29 Please start homework today Wednesday: Lab 4: Testing Statistical Hypotheses Office Hours: Tuesday: 1:30 PM 2:30 PM Thursday: 10:30 AM 11:30 AM
8.2 Tests Concerning Hypotheses About Means Review: One-Sample z Test for population mean One-Sample z Test for population proportion One-sample t Test Two-sample t Test Tests with paired data

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One-sample t Test for a single Mean: General Setting: X 1 , ., X n : SRS from (approximately) N(μ, σ ) μ is the unknown parameter of interest The null hypothesis is H 0 : μ = μ 0 The alternative hypothesis could be: H a : μ ≠ μ 0 (two-sided) H a : μ > μ 0 (one-sided) H a : μ < μ 0 (one-sided)
Setting up Hypotheses If an investigator wishes to demonstrate conclusively that a particular assertion is correct, or wants to see strong evidence for an assertion before taking action, that assertion should be incorporated in H a Please read page 346 in your textbook

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One-sided vs. two-sided If, based on previous data or experience, we expect increase , more , better , etc. ( decrease , less , worse , resp.), then we can use a one sided test. Otherwise, by default, we use two-sided. Key words: different , departures , changed ”…
Test Statistic For population mean when the data is N(μ, σ ): Notes: df = n 1 Measures compatibility between null hypothesis and data If n is large (≥30), CLT guarantees a approximate normal distribution and the t can be replaced with z , where z follows a standard normal distribution.

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## This note was uploaded on 02/06/2012 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue.

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Lecture20 - STAT 350 Lecture 19 & 20 8.2 Tests Concerning...

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