AP Statistics

This course is equivalent to a one-semester, introductory, non-calculus-based, college course in statistics. Statistics blends the rigor, calculations and deductive thinking of mathematics with the real-world examples and problems of the social sciences, the decision-making needs of business and medicine and the laboratory method and experimental procedures of the sciences. What students learn in this course will help them prosper in the 21st century.

Required Text

  • “Stats: Modeling the World” (can be found at Pearson Textbook) [e-text portal? If so, provide hyperlink]

Required Supplies

  • Lined paper/ notebook (8.5-by-11).
  • Three-ring binder highly recommended.
  • Graphing calculator TI-84 (provided for those who do not own one)
  • Writing utensil and highlighter

Course Format and Procedures

One to two quizzes will be given each week, ranging in duration from 20 to 40 minutes. Homework is assigned daily and constitutes 5% of quarter grade. After each chapter (see course outline) is completed, there will be a “homework assessment,” which cumulatively will constitute the 5% of the quarter grade.

Grading Procedures

  • Quizzes = 95%.
  • Mid-term exam: 10%

Student and Parent Resources

Course Outline

Part 1: Exploratory Data

Chapter 1: Stats Starts: Define statistics; examples of statistics activity; class survey

Chapter 2:  Data: Identify the who, what, why, where and how of data classification of categorical versus quantitative variables.

Chapter 3:  Displaying and Describing Categorical Data: Recognize categorical variables; display with a frequency table, bar chart, pie chart or contingency table; compare conditional and marginal percentages.

Chapter 4:  Displaying Quantitative Data: Recognize quantitative variables; display with stem and leaf plots, dot plots, histograms or time plots; describe distributions (gaps or clusters, shape, outliers, center, spread).

Chapter 5:  Describing Distributions Numerically: Select and calculate suitable measure of center and spread for quantitative variables; learn basic properties of mean, median and standard deviation; calculate mean, median, 5-number summary, standard deviation and interquartile range (IQR).

Chapter 6:  The Standard Deviation and the Normal Model: Calculate and interpret z-score; recognize appropriateness of a “normal model”; estimate probability through the use of normal models and the “empirical rule use” of z-table or appropriate technology to obtain percentages and probabilities.

Chapter 7:  Scatter plots, Association and Correlation: Define explanatory and responsive variables; create scatter plots of data; compute correlation between variables; describe direction, form and strength of linear associations; interpret statistical software produced by correlation tables.

Chapter 8:  Linear Regression: Identify regression equations, correlation, slope and intercept values from statistical software output and from summary statistics; predict a value of y of a given x from a regression equation; compute residuals; use residual plots to determine appropriateness of computing a regression.

Chapter 9:  Regression Wisdom Identify high leverage points and influential points; explain the impact of leverage and influential points on the regression; identify lurking variables; address the danger of extrapolating beyond the range of x-values used in regression.

Chapter 10:  Re-expression of Data: Model non-linear data activity. Explore exponential M+M’s

Part 2: Experimental Design

Chapter 11:  Understanding Randomness: Recognize random outcomes in real-world situations; design and perform simulations by generating random numbers on calculator or by using a random number table; draw conclusions from results of simulations.

Chapter 12:  Sample Surveys: Distinguish between samples versus populations; understand the pros and cons of various sampling methods (e.g., simple random sample, systematic sample, stratified sampling, cluster sampling, multistage sample and convenience sample); understand the various biases and how they impact survey results and conclusions (e.g., voluntary response , non-responsive, response, under-coverage).

Chapter 13:  Experiments and Observational Studies: Identify retrospective vs. perspective studies and the usefulness of each; identify the four basic principles of experimental design (control, randomization, replication and blocking); define experimental units, factors and treatments; design a completely randomized experiment – to test the effect of one or two factors; discuss ethics of experiments.

Midterm Review and Midterm

Part 3: Probability

Chapter 14:  From Randomness to Probability: Learn law of large numbers; define basic terms of probability (e.g., trial, outcome, event and complement); apply basic add/multi rules for probability; identify disjoint and independent events.

Chapter 15:  Probability Rules: Learn general addition and multiplication rules for non-disjoint and non-independent events; understand conditional probability; calculate probabilities through the use of Venn diagrams, two-way tables and tree diagrams.

Chapter 16:  Random Variables: Find the probability model for a discrete random variable; calculate the expected variable and variance of a random variable; determine mean and standard deviation after +/x by a constant; determine mean and standard deviation when +/- two independent random variables.

Chapter 17:  Probability Models: Identify Bernoulli trials; find expected value and probabilities of a geometric model; find mean and standard deviation of a Binomial model; estimate Binomial probability using a normal model.

Part 4: Inference

Chapter 18:  Sampling Distribution Models: Use a sampling distribution model to make statements about mean or distribution proportion; interpret the central limit theorem.

Chapter 19:  Confidence Intervals for Proportions: Construct a one-proportion z interval both mathematically and using statistical software; understand the impact of sample size and confidence level on the margin of error.

Chapter 20:  Testing Hypotheses about Proportions: State the null and alternative hypotheses for a one-proportion z test; understand differences between one-sided and two-sided alternative hypotheses; perform a one-proportion z test both mathematically and using statistical software; interpret the results of a one-proportion z test.

Chapter 21:  More About Tests: Understand the relationship between hypothesis tests and confidence intervals; choose an appropriate significance level (alpha level) with justification; identify Type 1 and Type 2 errors; define the power of a test.

Chapter 22:  Comparing Two Proportions: Find a confidence interval for the difference between two proportions; perform a two-proportion z test both mathematically and using statistical software; interpret the meaning of the calculated p-value.

Chapter 23:  Inferences about Means: Compute and interpret one-mean t interval using statistics software or from summary statistics; perform and interpret a one-mean t test using summary stats or statistical software; explain the difference between using a z-table and a t-table, define degrees of freedom.

Chapter 24:  Comparing Means: Perform and interpret a two-sample t test using software or a calculator; calculate and interpret a two-sample t interval using software or a calculator.

Chapter 25:  Paired Samples and Blocks: Recognize whether a design comparing two groups is paired; calculate and interpret a paired confidence interval; perform and interpret a paired t-test.

Chapter 26:  Comparing Counts: Display and interpret counts in a two-way table; use the chi-squared tables to perform and interpret chi-square tests; compute and interpret a chi-square test using software or a calculator.

Chapter 27:  Inferences for Regression: Test the standard hypothesis that the true regression slope is zero; state the null and alternative hypotheses; locate relevant numbers in a standard computer regression output; find a confidence interval for the slope of a regression based on the values reported in a standard regression output table