Contents
AP Score for the Diagnostic Exam
Study Guide for the Diagnostic Test Multiple-Choice Questions
THEME ONE: EXPLORATORY ANALYSIS
Bar charts; dotplots; histograms; stemplots; center and spread; clusters and gaps; outliers; modes; shape; cumulative relative frequency plots; skewness.
Topic Two: Summarizing Distributions
Measuring the center: median and mean; measuring spread: range, interquartile range, variance, and standard deviation; measuring position: simple ranking, percentile ranking, and z-score; empirical rule; histograms and measures of central tendency; histograms, z-scores, and percentile rankings; boxplots; effect of changing units.
Topic Three: Comparing Distributions
Dotplots; double bar charts; back-to-back stemplots; parallel boxplots; cumulative frequency plots.
Topic Four: Exploring Bivariate Data
Scatterplots; correlation and linearity; least squares regression line; residual plots; outliers and influential points; transformations to achieve linearity.
Topic Five: Exploring Categorical Data: Frequency Tables
Marginal frequencies and distributions; conditional frequencies and distributions.
Topic Six: Overview of Methods of Data Collection
Census; sample survey; experiment; observational study.
Topic Seven: Planning and Conducting Surveys
Simple random sampling; characteristics of a well-designed, well-conducted survey; sampling error: the variation inherent in a survey; sources of bias in surveys; other sampling methods.
Topic Eight: Planning and Conducting Experiments
Experiments versus observational studies versus surveys; confounding, control groups, placebo effects, and blinding; treatments, experimental units, and randomization; completely randomized design for two treatments; randomized paired comparison design; replication, blocking, and generalizability of results.
Topic Nine: Probability as Relative Frequency
The law of large numbers; basic probability rules; multistage probability calculations; binomial distribution; geometric probabilities; simulation; discrete random variables, means (expected values), and standard deviations.
Topic Ten: Combining Independent Random Variables
Means and variances for sums and differences of sets; means and variances for sums and differences of independent random variables.
Topic Eleven: The Normal Distribution
Properties of the normal distribution; using tables of the normal distribution; using a calculator with areas under a normal curve; the normal distribution as a model for measurement; commonly used probabilities and z-scores; finding means and standard deviations; normal approximation to the binomial; checking normality.
Topic Twelve: 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; the t-distribution; the chi-square distribution; the standard error; bias and accuracy.
THEME FOUR: STATISTICAL INFERENCE
Topic Thirteen: Confidence Intervals
The meaning of a confidence interval; confidence interval for a proportion; confidence interval for a difference of 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.
Topic Fourteen: Tests of Significance—Proportions and Means
Logic of significance testing, null and alternative hypotheses, P-values, one- and two-sided tests, Type I and Type II errors, and the concept of power; hypothesis test for a proportion; hypothesis test for a difference between two proportions; hypothesis test for a mean; hypothesis test for a difference between two means (unpaired and paired); more on power and Type II errors; confidence intervals versus hypothesis tests.
Topic Fifteen: Tests of Significance—Chi-Square and Slope of Least Squares Line
Chi-square test for goodness of fit; chi-square test for independence; chi-square test for homogeneity of proportions; hypothesis test for slope of least squares line; independence.
Relating Multiple-Choice Problems to Review Book Topics
Checking Assumptions for Inference
Table A: Standard Normal Probabilities
2 Critical Values