1. 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!

2. Left Tailed Right Tailed Two tailed
Reject Ho
Reject Ho
Reject Ho Accept Ho
Accept Ho Reject Ho
Accept Ho

3. 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.

4. 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).

5. 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)

6. 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)

7. 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)