- Parameter vs. statistic
- Central limit theorem.
If are independent
samples from a distribution with mean and standard deviation
, then
Hence, a convidence interval for is given by

where is the -quantile of

*N*(0,1). See Tables A.[23]. - For small sample size (e.g., n less than 30), the central limit
theorem does not hold. If the population is normally distributed,
one can still use the t-distribution to construct a confidence
interval for the mean, given the sample mean and sample standard
deviation.
- How to compare two alternatives:
- If the samples are paired, just compute the pairwise differences and test to see if the mean difference is significantly different from zero.
- If the samples are unpaired, we can
- Compute confidence intervals for each sample and see if they overlap; or
- Use a t-test as described in Section 13.4.2.

- all the examples in this chapter?
- how to use Tables A.2, A.3, A.4?
- why a confidence interval can be more useful than hypothesis testing?

CS 5014, C. J. Ribbens, 10/01/2001