**Sampling:**- Be prepared to answer at most one question on sampling techniques.
- Review different types of bias associated with various sampling methods.
- Review the handout on sampling from the textbook "Statistics" by Freedman, Pisani, and Purves.
- Know the central limit theorem and characteristics of populations that affect the sample size necessary for the sampling distribution to become approximately normal.

**Estimation:**- Know what the likelihood function is.
- Know how to find maximum likelihood estimates.
- Know how to define and evaluate properties of estimators, such as bias, standard error, and mean square error.
- Know the Rao-Cramer lower bound for unbiased estimators and the conditions under which it holds.
- Know how to calculate the information of a parameter.
- Know how to find a confidence interval for a population mean, and know when the t distribution and the normal distributions are appropriate.
- Review using the bootstrap (both nonparametric and parametric) to estimate standard errors or confidence intervals.

**Hypothesis Testing:**- Know the basic terminology including the terms null hypothesis, alternative hypothesis, p-value, test statistic, type I and type II errors, power, simple and composite hypotheses, etcetera.
- Know how to do standard problems about a single population mean or comparisons between population means.
- Be able to sketch the power of various hypothesis tests.
- Know how to do a likelihood ratio test.
- Recall how to calculate the Wilcoxon test statistic and how to find a p-value in principle in a test for the median of a distribution.
- Recall how to calculate the Wilcoxon test statistic for comparisons between two populations and know in principle how to compute a p-value.
- Recall the sign test for a median.
- Recall how to use the permutation test in various situations.

**Goodness-of-fit Tests:**- Know how to apply the chi-square goodness-of-fit tests to test the agreement with sample data with hypothesized probability distributions.
- Know in principle how to test for goodness-of-fit with a likelihood ratio test.
- Know how to calculate the Kolmogorov-Smirnov goodness-of-fit test statistic and how to compute a p-value in principle.
- Know how to do a chi-square test to test the independence of two discrete random variables.

**Regression:**- Know how to interpret S-PLUS regression output.
- Know how to examine residual plots to look for deviation from regression assumption.
- Know the formula for the least squares line slope and intercept in terms of the correlation coefficient and the standard deviations.

**Analysis of Variance:**- Know how to interpret S-PLUS ANOVA output.
- Know how to complete and ANOVA table from summary sample data.
- Know the assumptions for the F statistic to have an F distribution.
- Know how to find the various sums of squares and how to find their expectations.

Last modified: April 30, 1999

Bret Larget, larget@mathcs.duq.edu