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**Stat381 Cheat sheet: Confidence Intervals**

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

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**Left Tailed Right Tailed Two tailed**

Reject Ho Reject Ho Reject Ho Accept Ho Accept Ho Reject Ho Accept Ho

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**Quick recipe #1: One sample T test**

Hypothesis testing on the mean General procedure to test the hypothesis that Ho: µ= µo , when you have observed n values from a normal population. If you know the variance (σ²) Calculate sample mean X Calculate the statistic Z: At 5% significance level, accept Ho if Z is between and 1.96. Use normal dist. table to determine critical point at other significance levels. If you don’t known the variance Calculate sample mean X Calculate sample variance S² Calculate the statistic T: 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. Original formula for sample variance: Reference: Downing & Clark, Statistics: the easy way. Barron’s Educational Series, 1997.

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**Quick recipe #2: comparing two means with known variances (rarely used)**

Hypothesis testing on the difference between two means: known variances Null hypothesis: Ho: µ₁ - µ₂ =D, (D is often zero).

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**Quick recipe #3: T test with equal variances**

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

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**Quick recipe #4: T test with unequal variances**

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

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**Quick recipe #5: Paired T test**

Hypothesis testing on the difference between two means: Paired data Null hypothesis: Ho: Normality required In EXCEL: TTEST(array1,array2,tails,1)

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