AP Statistics Syllabus

Course Introduction

This AP Statistics course is designed to introduce students to the main topics of a freshman-level college statistics course. It emphasizes understanding of concepts, statistical language, and statistical techniques. The course requires a practical understanding of statistical tools including the TI83/84 graphing calculator and Minitab statistical software, which will be implemented throughout the course. Students are expected to effectively use experimental design, data analysis, and inference to reach well-reasoned and appropriately communicated conclusions and decisions in a real-world context.

Grading

Six weeks grades will be determined as follows:      

Tests – 70%

Quizzes, Daily and Homework – 30%

The semester exam will constitute 10% of the semester average.

There will be a test at the end of each instructional unit.

Quizzes will be given periodically – either announced or unannounced – in order to evaluate the students’ knowledge of the material on a day-to-day basis.

Resources

The Practice of Statistics Second Edition by Daniel Yates, David Moore, Daren Starnes; W.H. Freeman and Company; 2002.

TI-83 or TI-84 Graphing Calculator

Decisions Through Data Video Series

Teacher created worksheets and handouts

Computers for using Minitab and Microsoft Excel

Computer output from popular software packages

Fall Semester:

Exploring Univariate Data – Chapter 1

The student will

• Identify types of data and associated graphs
• Construct and compare displays including dot plot, stem plot, histogram, cumulative frequency plot, bar graph, pie graph, time plot, and boxplot (By hand and using graphing calculator capabilities)
• Interpret and/or graphical displays including shape, center, spread, clusters and gaps, outliers, and unusual features using the graphing calculator. Be able to interpret graphs using appropriate language
• Summarize distributions using appropriate measures for center, shape, and spread
• Calculate and interpret standard deviation as a measure of spread using TI-83 and interpreting the results using correct vocabulary
• Evaluate the effect of changing units of measure on summary statistics
• Project: Fast Food Comparisons of nutritional values using data analysis with graphs

Counting Techniques and Probability – Chapter 6

The student will

• Apply basic probability concepts including permutations, combinations, sample spaces and Venn diagrams (Use graphing calculator for permutations/combinations)
• Develop and apply the addition and multiplication rules for probability including exclusiveness and independence

The Normal Distribution – Chapter 2

The student will

• Examine properties and calculate probability for non-normal density curves
• Examine properties of the normal distribution including the empirical rule
• Use the normal curve to calculate probabilities and determine observed values. Using graphing calculator statistics capabilities to calculate probabilities.
• Assess the normality of a distribution by graphing data with graphing calculator and also be able to express in words correctly.

Examining Relationships – Chapter 3

The student will (using the graphing calculator)

• Draw conclusions about bivariate data by analyzing and displaying patterns in scatterplots and express the findings in a meaningful coherent manner.
• Determine and analyze the correlation coefficient and its implications on linearity
• Determine the least squares regression line and its coefficient of determination
• Construct and analyze the residual plot for the least squares regression line (LSRL) including outliers and influential points

More on Two–Variable Data – Chapter 4

The student will (using the graphing calculator)

• Transform non-linear data to achieve linearity – log and power transformations, piecewise functions
• Analyze and describe relationships between two or more categorical variables, including Simpson’s Paradox
• Investigate the role of lurking variables in effecting association

Producing Data:  Samples and Experiments – Chapter 5

The student will

• Compare and contrast methods of data collection including census, samples, experiments and studies.
• Analyze characteristics of a well-designed and conducted survey.
• Identify and perform a variety of sampling designs including simple and stratified random sampling.
• Analyze characteristics of a well-designed and conducted experiment including control, randomization and replication.
• Understand the significance of treatments, experimental units, control groups, random assignments and replication in designed experiments.
• Determine possible sources of bias and confounding and the need for the placebos and blinding.
• Design completely randomized experiment and blocked experiment including matched pair design
• Perform experiments using the graphing calculator to generate simulations.
• Students will be able to effectively explain the process and findings of the experiments

Probability Revisited – Chapter 6

The student will

• Determine the probability of relative frequency using the “law of large numbers” concept.
• Apply the addition rule, multiplication rule, conditional probability, and independence to determine probability as relative frequency.
• Connect trees and tables to conditional probability concepts.

Random Variables – Chapter 7 (Using the graphing calculators statistical programs)

• Understand and apply probability with discrete random variables and their probability distributions.
• Understand and apply mean (expected value), standard deviation and linear transformation of a random variable.
• Understand and apply probability with mean and standard deviation for sums and differences of independent random variables including the notion of independence versus dependence.
• Be able to explain findings with a thorough understanding of the statistical language

The Binomial and Geometric Distributions – Chapter 8 (Using the graphing calculators statistical programs)

• Apply formulas or simulations to determine binomial and geometric probability.
• Understand and apply mean and standard deviation of a binomial random variable.
• Use the normal distribution to approximate a binomial distribution.

Spring Semester:   Students will use the graphing calculators to perform all tests of significance and confidence intervals with a formal write up and presentation.

Sampling Distributions - Chapter 9

• Apply the Central Limit Theorem to distribution of sample means.
• Define aspects of the sampling distribution of sample means using simulations.
• Determine mean and standard deviation of a sampling distribution of means.
• Project: Bivariate Analysis.

Introduction to Significance Tests and Inferences – Chapters 10-15.

Develop the concept of confidence interval including the relationship between the interval size and confidence level.

• Determine a confidence interval for a sample mean.
• Explore the relationship between sample size and margin of error.
• Perform tests of significance for a mean (z test) including the logic of significance testing, null and alternative hypotheses, p-values, one-and-two sided tests. and conclusions.
• Explore the consequence of a type 1 and type 2 error as well as their relationship to the power of a test.

Inferences for one sample distributions

• Examine the properties of the t-distribution including calculating t-values and probabilities.
• Determine confidence intervals and perform tests of significance for a sample mean with unknown standard deviation.
• Determine confidence intervals and perform tests of significance for a matched pair design.
• Define aspects of the sampling distribution of a sample proportion.
• Determine the confidence interval for a large sample proportion.
• Perform tests of significance for a large sample proportion.

Inferences for two sample distributions

• Determine the confidence interval for the difference between two sample means.
• Perform tests of significance for the difference between two sample means.
• Determine confidence intervals for the difference between two proportions.
• Perform tests of significance for the difference between two proportions.

Chi-square procedures

• Employ the chi-square test for goodness of fit, homogeneity of proportions, and independence

Inference for Regression

• Investigate and perform inference for the slope of the least squares regression line (LSRL).
• Interpret computer print-outs from statistical software.

Review for AP exam – (Teacher generated) 6 Major Topic Reviews

          Currently released AP Multiple Choice Exam

ANOVA Procedures for after the exam.