AP Statistics



AP Statistics

Instructor: T. Teclaw Room: C 204

Text : Yates, Daniel S., Moore, David S., and Starnes, Daren S., The Practice of Statistics, TI-83/84 Graphing Calculator Enhanced; Third Edition, W.H. Freeman and Company 2008

Description of Course:

Students who are interested in math, all sciences, engineering, business, psychology and other college programs will find this course valuable. Students will study the application and interpretation of statistical measures of central tendency, graphical displays of data to study patterns and deviation from patterns. They will design surveys and experiments, gather data, display results graphically and numerically, and apply inferential statistics to draw conclusions for a population. Probability will be used for anticipating what the distribution of data should look like under a given model of various models and its implications. The students will be able to integrate all of the above topics to estimate population parameters and test hypotheses.

The course will be comprised of four major topics of study:

• Descriptive Statistics—Chapters 1-4

• Producing Data—Chapter 5

• Probability—Chapters 6-8

• Inferential Statistics—Chapters 9-13

Students will be working independently or together in small groups at times, and will learn appropriate terminology to be able to clearly communicate and discuss graphs, numerical data, methodology and inferences using appropriate statistical terminology.

Technology:

• It is highly recommended all students have a TI-83/84+ graphing calculator. There will be a class set of TI-Nspire graphing calculators available for students to use during class and either before or after school. However, it is best for students to have their own calculator; it will be used extensively throughout the course and on the AP Statistics exam.

• Access to the Internet for applets and videos.

Assignments:

Each chapter students will receive a list of assignments.

Projects:

Students will complete 2-3 projects per semester, in which students will use appropriate statistical terminology describing methodology, results and interpretations of those results.

Course Outline: (According to chapters in textbook)

Chapter 5: Producing Data

▪ Types of data, sampling, and bias

▪ Simple random samples

▪ Stratified random samples

▪ Cluster sampling

▪ Experimental design including block and matched pairs

▪ Randomization

▪ Treatments, control groups and blocking

▪ Use random digits table and/or graphing calculator to run simulations

Chapter 1:

▪ Displaying univariate data: bar charts, dotplots, stemplots, boxplots, frequency charts, histograms, cumulative frequency charts (ogives)

▪ Using the graphing calculator to create graphical displays

▪ Interpret the graphs in terms of shape, center and spread as well as gaps and outliers

▪ Calculate numerical descriptions of data: mean, median, five-number summary, range, interquartile range, standard deviation, variance

▪ Outliers

▪ Interpret numerical measures in context of the situation

▪ How to write an interpretation in paragraph form

▪ Comparisons of univariate data within group and between groups

▪ Linear transformations of data

Chapter 2:

▪ Compute measures of relative standing using z-scores and percentile ranks

▪ Apply concepts of density curves including its mean and median

▪ Demonstrate understanding of Normal distributions and the 68-95-99.7 Rule

▪ Use tables and the graphing calculator to find the proportion of values on an interval of the Normal distribution with a given proportion of observations either above or below it

▪ Assess the normality of a distribution using a Normal probability plot

Chapters 3 and 4:

▪ Make and describe scatterplots

▪ Compute and interpret the correlation coefficient

▪ Explain the least squares regression line

▪ Demonstrate an understanding of r, r2 and the least squares regression line in context of the situation

▪ Use residual plots and the coefficient of determination to measure the quality of the least squares regression line

▪ Discuss the significance of unusual and influential points

▪ Modeling non-linear data: logarithmic and power transformations

▪ Describe the parts of a two-way table

▪ Give and identify an example of Simpson’s Paradox

▪ Identify the criteria for causation

Cumulative Exam Chapters 1-5

Chapter 6:

▪ Definition of probability

▪ Conduct a simulation with and without the graphing calculator

▪ Properties of probability

▪ Independence

▪ Addition and multiplication rule

▪ Intersection and union of events

Chapter 7:

▪ Properties of discrete random variables

▪ Properties of continuous random variables

▪ Describe the law of large numbers

▪ Calculate the expected value (mean) of a discrete random variable

▪ Calculate the variance and standard deviation of a discrete random variable

▪ Perform linear combinations of two random variables

Chapter 8:

▪ Describe what is meant by a binomial distribution

▪ Calculate the mean and standard deviation of a binomial random variable

▪ Use the TI-83/84+ binomial distribution menu

▪ Solve a binomial using a Normal approximation

▪ Describe what is meant by a geometric distribution

▪ Calculate the mean and standard deviation of a geometric random variable

First Semester Review

Chapter 9:

▪ Define sampling distributions

▪ Contrast bias and variability

▪ Describe the sampling distribution of a sample proportion

▪ Describe the sampling distribution of a sample mean

▪ Explain the central limit theorem

▪ Solve probability problems involving the sampling distribution of a sample mean

▪ Use a Normal approximation to solve probability problems

Chapter 10:

▪ Statistical inference

▪ Describe the form of all confidence intervals

▪ Confidence interval for a population proportion

▪ Confidence interval for a population mean

▪ Margin of error and ways to control its size

▪ Finding a sample size

▪ Use the t-distribution

▪ Checking conditions necessary to conduct a confidence interval

▪ Standard error of [pic]

Chapter 11:

▪ Tests of significance

▪ Forming hypotheses

▪ Types of errors in testing

▪ Discuss the power of a test

▪ P-values

Chapter 12:

▪ Conduct one-sample and paired data t significance tests

▪ Explain the differences between the one-sample confidence interval for a population proportion and the one-sample significance test for a population proportion

▪ Conduct a significance test

Chapter 13:

▪ Conditions needed for inference in comparing two population means

▪ Confidence intervals and significance test for difference between two population means

▪ Conditions needed for inference in comparing two population proportions

▪ Confidence intervals and significance test for difference between two population proportions

Chapter 14:

▪ The chi-square distribution and goodness of fit test

▪ Given a two-way table, compute conditional distributions

▪ Conduct a chi-square test for homogeneity of populations

▪ Conduct a chi-square test for association/independence

▪ Use the graphing calculator chi-square menu

Chapter 15:

▪ Conditions necessary for inference for regression

▪ Standard error and confidence interval for the least-squares regression line

▪ Using the graphing calculator

Review for AP Exam and Final Exam

Supplemental study after the AP Exam: ANOVA

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