### Confidence Intervals: Comparing Systems Using Sample Data

#### What should I know?

• 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.

#### Can you explain ...

• 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