## Exam Topics

- Describing Patterns in Data

Univariate data: dotplot, stemplot, histogram, cumulative frequency plot, center and spread, clusters and gaps, outliers, median, mean, range, interquartile range, standard deviation, quartiles, percentiles, standardized z scores

Comparing distributions of univariate data: dotplots, back-to-back stemplots, parallel boxplots, comparing center and spread within group and between group variation, comparing clusters and gaps, comparing outliers

Bivariate data: analyzing patterns in scatterplots, correlation and linearity, least-squares regression line, residual plots, outliers and inﬂuential points, transformations to achieve linearity by logarithmic and power transformations

Categorical data: frequency tables, bar charts, marginal and joint frequencies for two-way tables, conditional relative frequencies and association, comparing distributions using bar charts

- Sampling and Experimentation

Data collection: census, sample survey, experiment, observational study

Conducting surveys: characteristics of well-conducted survey, populations, samples and random selection, sources of bias in sampling and surveys, sampling methods of simple random sampling, stratified random sampling and cluster sampling

Conducting experiments: characteristics of well-conducted experiment, treatments, control groups, experimental units, random assignments and replication, sources of bias and confounding, placebo effect and blinding, completely randomized design, randomized block design, matched pairs design

Generalizability of results and types of conclusions that can be drawn from

observational studies, experiments and surveys

- Probability Distributions

Probability: interpreting probability, including long-run relative frequency interpretation, law of large numbers, addition rule, multiplication rule, conditional probability and independence, discrete random variables and their probability distributions, binomial and geometric distributions, simulation of random behavior and probability distributions, expected value and standard deviation of a random variable, linear transformation of a random variable

Combining independent random variables: independence versus dependence, mean and standard deviation for sums and differences of independent random variables

Normal distribution: properties, tables of the normal distribution, normal distribution as a model for measurements

Sampling distributions: sampling distribution of a sample proportion, sampling distribution of a sample mean, central limit theorem, sampling distribution of a difference between two independent, sample proportions, sampling distribution of a difference between two independent

sample means, simulation of sampling distributions, t-distribution, chi-square distribution

- Statistical Inference and Hypothesis Testing

Point estimators and confidence intervals: estimating population parameters, margins of error, properties of point estimators, unbiasedness and variability, meaning of confidence level and confidence intervals, properties of confidence intervals, large sample confidence interval for a proportion, large sample confidence interval for a difference between two proportions, confidence interval for a mean, confidence interval for a difference between two means, confidence interval for the slope of a least-squares regression line

Tests of significance: logic of significance testing, null and alternative hypotheses, p-values, one- and two-sided tests, type I and type II errors, power, large sample test for a proportion, large sample test for a difference between two proportions, test for a mean, test for a difference between two means (unpaired and paired), chi-square test for goodness of ft, homogeneity of proportions, and independence (one- and two-way tables), test for the slope of a least-squares regression line

## Exam Format

Section I: Multiple choice, 40 questions, 1 hour 30 minutes, 50% weight

Section II: Free response, 6 questions, 1 hour 30 minutes, 50% weight