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Stat381 Cheat sheet: Confidence Intervals Parameters being estimated Begin Derivation with Distribution (D.F.) 100(1-α)% conf. interval 1 © 2008 Xijin Ge, All rights NOT reserved. Accuracy NOT guaranteed!

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Reject H o Accept H o Accept H o Reject H o Accept H o Reject H o Left Tailed Right Tailed Two tailed http://www.pindling.org/Math/Statistics/Textbook/Chapter8_two_population_inference/proportion_independent.htm http://library.beau.org/gutenberg/1/0/9/6/10962/10962-h/images/069.png

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Hypothesis testing on the mean General procedure to test the hypothesis that H o : µ= µ o, when you have observed n values from a normal population. If you know the variance (σ²) 1.Calculate sample mean X 2.Calculate the statistic Z: 3.At 5% significance level, accept H o if Z is between -1.96 and 1.96. 4.Use normal dist. table to determine critical point at other significance levels. If you don’t known the variance 1.Calculate sample mean X 2.Calculate sample variance S² 3.Calculate the statistic T: 4.The T statistic will have a T dist. with n- 1 degree of freedom if the null hypothesis is true. Make decision based on table, in the context of left, right or two tailed test. Reference: Downing & Clark, Statistics: the easy way. Barron’s Educational Series, 1997. Quick recipe #1: One sample T test Original formula for sample variance: 3

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Hypothesis testing on the difference between two means: known variances Null hypothesis: Ho: µ₁ - µ₂ =D, (D is often zero). Quick recipe #2: comparing two means with known variances (rarely used) 4

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Hypothesis testing on the difference between two means: equal variances Null hypothesis: Ho: µ₁ - µ₂ =D, (D is often zero). Quick recipe #3: T test with equal variances In Excel: TTEST(array1,array2,tails,2) Normality required 5

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Hypothesis testing on the difference between two means: unequal variances Null hypothesis: Ho: µ₁ - µ₂ =D, (D is often zero). Quick recipe #4: T test with unequal variances In EXCEL: TTEST(array1,array2,tails,3) Normality required. Safe to use even variances equal. 6

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Hypothesis testing on the difference between two means: Paired data Null hypothesis: Ho: Quick recipe #5: Paired T test In EXCEL: TTEST(array1,array2,tails,1) Normality required 7

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