1. Inference for Distributions
Chapter 11

2. Inference for the Mean of a Population
Section 11.1
Inference for the Mean of a Population

3. Conditions for Inference about a Mean
Data are a SRS from population of interest
Observations from population have a normal distribution

4. Standard Error
The standard deviation of a statistic is estimated from the data
s/n

5. If  is known, use one-sample z-statistic
If  is not known, use one-sample t-statistic
t distributions with n – 1 degrees of freedom

6. Facts about t Distribution
Density curves are similar in shape to the standard normal curve
Symmetric about zero, single-peaked, and bell-shaped

7. Spread is greater than standard normal distributions
As degrees of freedom k increase, the t(k) density curve approaches the N(0, 1) curve ever more closely

8. Confidence Interval x bar ± t* (s/n)
t* is upper (1 – C)/2 critical value for the t(n –1) distribution

9. The Three C’s Interpretation of results
Conclusion, connection, and context

10. Matched Pairs t Procedures
To compare the responses to the two treatments in a matched pairs design, apply the one-sample t procedures to the observed differences
The parameter  is the mean difference in response to the two treatments within matched pairs of subjects in the entire population

11. Robust Procedure
A confidence interval or significance test is called robust if the confidence level or P-value does not change very much when the assumptions of the procedure are violated

12. t procedures are strongly influenced by outliers

13. Using t Procedures SRS from population of interest
SRS normal distribution
Sample size less than 15 ~ use t procedures if the data are close to normal

14. Sample size at least 15 ~ use t procedures unless outliers are present or there is strong skewness
Large sample ~ use t as long as sample is large, roughly n  40

15. Practice Problems
pg. 642 #