Download AP Statistics

COURSE OUTLINE
AP STATISTICS
2014-2015
Text The Practice of Statistics: TI-83/84/89, TI-Nspire Graphing Calculator Enhanced 3rd ed.
Yates, Moore, and Starnes.
Throughout the course students will learn to use Fathom, SPSS, and Microsoft Excel in addition to
becoming proficient with their graphing calculators.
Organizing Data
Exploring Data
1. Introduction - What are Data, Variables, and Distributions? Using the calculator to manage data.
2. Displaying Distributions with Graphs. Graphing by hand and on a graphing calculator.
Introducing the description of distributions including center, spread, shape, skewness, outliers,
clusters, gaps, etc.
a. Bar graphs, pie charts, dot plots, stemplots (incl. back to back)
b. Frequency distributions, histograms, ogives, and percentiles.
3. Describing Distributions with Numbers. Measures of center and spread and their
interrelationships. Emphasis on when certain measures are appropriate.
a. Measures of center – the mean and median
b. Measures of spread – std dev, range, IQR, boxplots, outliers.
c. Data Transformations – effect of linear transformations
d. Time Plots and comparing distributions
Normal Distribution
1. Density curves and normal distributions
a. Density curves, introduction
b. Normal distributions and empirical rule
2. Standard Normal Calculations
a. Z-scores and area under the curve
b. Finding z-scores from areas/proportions and assessing normality
Examining Relationships
1. Scatterplots
a. Explanatory/Response variables and positive/negative associations
2. Correlation
a. Calculation of r
b. Understanding and interpreting r.
3. Least-Squares Regression
a. Modelling and regression, the equation of the line, predicted value
b. R-squared and residuals – emphasizing the proportion of variability
c. Outliers and Influential Observations and residual plots
More on two variable data
1. Log and power transformations
2. Cautions about correlation and regression
a. Extrapolation and lurking variables
b. Types of association and causation
3. Relations in categorical data
a. Two way tables, marginal and conditional distributions, bar graphs and segmented bar
graphs.
b. Simpson’s paradox
Producing Data
Producing Data
1. Designing samples and the relationship between populations, samples, and censuses.
a. Observational studies versus experiments
b. Types of samples and BIAS. SRS, stratified, etc.
c. Using random number tables/generators to choose a sample.
d. Cautions about sampling – undercoverage, non response, and others
2. Designing Experiments – How to design and present a truly randomized experiment both in
diagram and paragraph forms.
a. Vocabulary and principles of randomized design including randomization, replication,
and control. Treatments, units (subjects), placebo effects and double blinds.
b. Matched pairs and block design
3. Simulating Experiments – Designing and executing probability models to simulate the
outcomes of experiments
Probability
Probability
1. Introduction – the concept of randomness. Probability as “long-run” behavior.
2. Probability Models – Sample space. Probability rules including addition and multiplication
rules. Concepts of independence, complements, and disjointedness.
3. General Probability – Venn diagrams and sets, conditional probability, tree diagrams and
Bayes’s rule.
Random Variables
1. Discrete and continuous random variables
a. Discrete R.V.s – probability distributions and graphical methods
b. Continuous R.V.s - emphasis on the connection with the normal distributions
2. Means and variances of random variables –
a. Mean and variance of discrete random variables
b. Law of Large Numbers
c. Means and variances of sums/differences and linear transformations of discrete and
continuous rvs.
Binomial and Geometric Distributions
1. Binomial distributions
a. Binomial setting and calculations of probabilities – Recognizing the binomial setting and
calculate probabilities and cumulative probabilities
b. Mean and standard deviation of a binomial variable
c. The normal approximation and simulation of binomial experiments
2. Geometric distributions
a. The geometric setting and calculating geometric probabilities
b. Expected value for geometric experiments
Sampling Distributions
1. Sampling distributions –
a. definition of a sampling distribution and introduction to the concept of an unbiased
statistic.
b. Variability and bias
2. Sampling Distribution of Sample Proportions
a. Mean and Standard Deviation of Sample Proportion
b. Rules of Thumb for the use of the normal approximation – emphasize the importance of
meeting conditions for the use of certain statistical tools
3. Sampling Distribution of sample means – emphasize the difference between the mean and
the distribution of means.
a. Mean and standard deviation of x-bar from a normal population
b. Central Limit Theorem
Inference
Introduction to Inference
1. Introduction to confidence intervals – constructing confidence intervals for the population
mean when sigma is known. Uses z*, introduces the concept of margin of error, the meaning
of confidence intervals, and conditions for their use
Calculation of confidence intervals and their behavior
a. Conditions and the structure of inference. Choosing sample size.
2. Tests of Significance – Significance tests for the population mean where sigma is known.
a. General outline of a significance test
b. The null and alternative hypotheses
c. P-Values and significance
d. The structure of a test and conditions
e. One-sided, two-sided tests and confidence intervals.
3. Cautions about significance testing including choosing significance levels, practical
significance, and multiple analyses.
4. Inference as decision – Type I, Type II errors, significance levels and power.
Inference for Means – confidence intervals and significance tests using the t-distributions. Using tables
and calculator to find p-values from t and vice versa.
1. Inference for a single mean
a. Conditions, standard error, the t-distributions, and degrees of freedom
b. t-confidence intervals and tests
c. Matched pairs procedures
d. Robustness and power of t-procedures
2. Inference for two means
a. Conditions, standard error and the procedures
Inference for proportions
1. Inference for a single proportion
a. Conditions and procedures, standard error for p-hat
b. Choosing sample size.
2. Inference for two proportions
a. Conditions, standard error and the procedures
3. REVIEW – how to select the right test for the right job: means and proportions. Revisiting
errors in testing.
Chi Square procedures.
1. Chi-square test for goodness of fit.
a. The chi-square distributions – Using calculator, computer and tables to understand chisquare distributions and the relation to degrees of freedom.
b. The goodness of fit test – expected value and calculating chi-square.
2. Chi square test for 2-way tables. Conditions and procedures. Expected values and degrees of
freedom
a. Test for homogeneity of multiple populations
b. Test for independence of two variables
Inference for Regression – inference for the slope of a line
1. Regression models and standard error. Conditions for inference about slope
2. Confidence intervals for the slope
3. Significance test for the slope
Possible Post AP Test Topics (choice varies depending on students’ interest and ability level)
1. Multiple Linear Regression using statistical software
2. ANOVA (Analysis of Variance)
3. Other probability distributions (hypergeometic, poisson, etc.)
4. F-test and the F-statistic