Download AP Statistics Syllabus

AP Statistics Syllabus
Instructor:
Josh Lamb
Textbook:
Stats – Modeling the World, AP edition, 3rd edition, by Bock, Velleman, and De Veaux,
Pearson – Addison Wesley, 2010.
Course Description:
Statistics is the art and science of collecting, organizing, analyzing, and drawing
conclusions from data. In AP Statistics, we will focus on four major themes: exploratory data analysis,
designing studies, probability models and simulations, and statistical inference. AP Statistics is designed
as the equivalent of a one-semester, introductory statistics course.
In this course, students develop strategies for collecting, organizing, analyzing, and drawing conclusions
from data. Students design, administer, and tabulate results from surveys and experiments. Probability
and simulations aid students in constructing models for chance phenomena. Sampling distributions
provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-84
graphing calculator statistical software output, and activities to investigate statistical concepts. To
develop effective statistical communication skills, students are required to prepare frequent oral
analysis of real data.
Course goals:
(1) To help you become an educated consumer of data and statistical claims
(2) To introduce you to the practice of doing statistics. Along the way, I hope you will see the
many and varied applications of statistics in medicine, business, psychology, environmental
science, and other important fields.
(3) To prepare you to take the AP Statistics exam in May.
Inside the Classroom: Since AP Statistics places equal importance on the accuracy of your statistical
methodology and the quality of your statistical communication, I will design investigations and
assignments that allow you to develop your skills in both these areas. There will be frequent writing
assignments based on real data, statistical analyses, and research studies. I will lecture very selectively.
My preferred method is to provide you with data to examine, simulations to perform, and guided
activities to tackle that will deepen your understanding of key techniques and concepts. In short, I
expect you to participate actively in all course activities. In addition, all students will be working through
problems sets in assigned small groups to foster communication skills in the subject matter.
Outside the Classroom: I assign homework. You are expected to attempt every problem I assign
conscientiously and deliberately. You will collaborate with your peers on a long term project. I will
insert several checkpoints along the way to ensure that you are making satisfactory progress. These
projects require students to design surveys and experiments, gather data, analyze the data numerically
and graphically, and apply inferential statistics to draw conclusions for a population. Students write
formal reports on their projects using statistical language.
Technology: The graphing calculator offers you a variety of tools for entering, storing, sharing,
displaying, analyzing, simulating and comparing sets of data. The World Wide Web offers interactive
java applets, data sources, and sites with a variety of statistical information. Technology will be an
integral component of this class that you must learn to use to your advantage. Certain class days will be
designated “Lab Days” where you will use statistical software and the internet to gather and analyze
data.
Course Content
Textbook
Correlation
Unit 1: Exploring and Understanding Data
Displaying and Describing Categorical Data – Frequency tables; the area principle; bar
charts; pie charts; contingency tables; conditional distributions; segmented bar charts;
Simpson’s paradox
Displaying Quantitative Data – Histograms; stem-and-leaf displays; dotplots; shape,
center, and spread; comparing distributions; timeplots
Skill: Making a histogram on the calculator
Describing Distributions Numerically – Median, IQR, and 5-number summary; making
and comparing boxplots; mean and standard deviation; variability; determining which
summary statistic to use when
The Normal Model – Standardizing with z-scores; how shifting and rescaling data effect
shape, center, and spread; 68-95-99.7 rule; z-scores for percentiles; normal probability
plots; assessing normality
Skill: Finding normal percentiles using the calculator
21 days
SMW
Ch3
Unit 2: Exploring Relationships Between Variables
Scatterplots, Association, and Correlation – Describing scatterplots; explanatory vs.
response variable; properties of correlation
Skill: Making a scatterplot using a calculator
Linear Regression – The linear model; residuals; least squares regression line (LSRL);
interpreting correlation; r2 – the variation accounted for; properties of r2; interpreting
the slope and y-intercept and r2 in context; Properties of the LSRL
Skills: Calculator discovery of the LSRL properties; computing residuals and making
residual plots on the calculator
Regression Wisdom – Subsets within data; prediction vs extrapolation; outliers,
leverage, and influential points; lurking variables and causation; summary values less
variable than individual values
Re-expressing Data – Straightening relationships; goals of re-expression; the ladder of
powers; power models – log x, log y transformations; exponential models – log y
transformations; choosing the best model – residuals and r2
Skill: Transformation and regression models on the calculator
23 days
SMW
Ch7
SMW
Ch4
SMW
Ch5
SMW
Ch6
SMW
Ch8
SMW
Ch9
SMW
Ch10
Unit 3: Gathering Data
Understanding Randomness – Making and conducting simulations
Skill: Using random digits and using the calculator to help carry out simulations
Obtaining Good Samples – Simple random sample (SRS); stratified sampling; cluster
sampling, systematic sampling, multi-stage sampling
Sampling – sample size; census; populations and parameters vs samples and statistics;
sampling badly – voluntary response; convenience sampling;
Designing and Implementing Surveys – Questions: wording, type, order; administration
methods; response bias; undercoverage and nonresponse bias
Experiments and Observational Studies – observational studies vs randomized
comparative experiments; s; control treatments; blinding; placebos; blocking; factors;
confounding variables vs. lurking variables
Basics of Experimental Design – Subjects, factors, treatments, explanatory and
response variables, placebo effect, blinding; completely randomized design (CRD);
diagrams
Principles of Experimental Design – control, random assignment, replication
More Advanced Experimental Designs – Multi-factor experiments; block designs; why
block?; difference between blocking and stratifying; matched pairs design
15 days
SMW
Ch11
SMW
Ch12
Unit 4: Randomness and Probability
Basic Probability Concepts – Probability as long-run relative frequency; randomness;
legitimate probability models; sample spaces, outcomes, events; law of large numbers
Basic Probability Rules – Addition rule for disjoint events; complement rule;
“something has to happen” rule
Probability Rules – General addition rule, Venn diagrams, union and intersection;
general multiplication rule, definition of independence; conditional probability, tree
diagram; disjoint vs. independent
Random Variables – Discrete vs. continuous
Discrete Random Variables – expected value and standard deviation
Rules for means and Variances – linear transformations of a single variable, linear
combinations of random variables, independence
Continuous Random Variables – Combining normal random variables, calculating
probabilities
Binomial and Geometric Random Variables – Bernoulli trials; probability density
function (pdf) vs. cumulative density function (cdf)
Geometric Distributions – X = # of trials up to and including 1st success; calculating
geometric probabilities; expected value of geometric random variable
Binomial Distributions – X = # of successes; calculating binomial probability; finding
mean and standard deviation for a binomial random variable
Normal Approximation – Estimating binomial probabilities with normal calculations
Skill: Geometric and Binomial distributions on the calculator
17 days
SMW
Ch14
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Ch13
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Ch15
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Ch16
SMW
Ch17
Unit 5: From Data at hand to the World at Large
Sampling Distribution Models – Moving toward inference; definition of sampling
distribution; standard error
Sampling Distribution of p̂ - Mean and standard deviation of sampling distributions;
normal approximations; assumptions and conditions – SRS, sample size is < 10% of
population, success/failure condition
Sampling Distribution of x - Mean and standard deviation of sampling distribution;
Central Limit Theorem (CLT); assumptions and conditions – SRS, independence, 10%
condition, large enough sample condition
Confidence Intervals for Proportions – confidence intervals to estimate a population
proportion, p
Estimating an Unknown Parameter – The idea of a confidence interval; connection
with sampling distributions; margin of error; critical values
Confidence Interval Considerations – Changing confidence level; interpreting CI vs.
interpreting confidence level; determining sample size; assumptions and conditions –
independence, SRS, 10% condition, success/failure condition
Skill: Calculate a one-proportion interval on the calculator
Testing Hypothesis About Proportions – Significance tests with the inference toolbox
Tests of Significance – underlying logic of significance tests; stating hypotheses; one
tailed vs. two-tailed tests; P-values vs. fixed significance levels
Skill: One proportion z-test on calculator
More About Tests – Definition of “statistically significant”; significance level, critical
value
Type I and II Errors, Power – Type I and II error in context; connection between power
and Type II error
Estimating the Difference Between Population Proportion
Testing a Claim about the Difference Between Population Proportions – Using the
pooled proportion as an estimate
Skill: Two-proportion inference on the calculator
17 days
SMW
Ch18
Unit 6: Inference about Population Means
Statistical Inference for Mean – Describing sampling distributions of sample means
using a model selected from the t-distributions based on degrees of freedom; variability
in sample means is the standard error; margin of error for a confidence interval; testing
hypothesis about population means; checking assumptions
Skill: Performing t procedures on the calculator
Statistical Inference to Compare the Means of two Independent Groups – t-models;
checking assumptions; standard error for the difference between two means; twosample t intervals and two-sample t-tests
Skill: Performing two-sample t procedures on the calculator – different df
Paired Samples and Blocks – matched pairs vs. two independent samples
11 days
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Ch23
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Ch19
SMW
Ch20
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Ch21
SMW
Ch22
SMW
Ch24
SMW
Ch25
Unit 7: Inference When Variables are Related
Chi-Square Goodness of Fit Test – The chi-square family of curves
Chi-Square Test of Homogeneity – Independent SRSs or randomized experiments
Chi-Square Test of Association/Independence – Distinguishing between homogeneity
and association/independence questions
Activity: M&M color distributions
Inference about Linear Regression – Population vs. sample regression lines
Confidence Intervals and Significance tests about β – Nasty formulas; computer
output; abbreviated inference toolbox
Skill: Regression inference on the calculator
AP EXAM Review – 20 Days
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Chapter 1-27 Review
Practice AP Free Response Questions
Practice Released AP Multiple Choice Questions
Grading Procedures/Rubric Review
12 days
SMW
Ch26
SMW
Ch27