Advanced Placement Statistics
Syllabus
Lynn Ferguson
Greenup County High
Primary Textbook: Yates, Daniel, Moore, David, and Daren Starnes. The Practice of
Statistics, third edition. New York: W.H. Freeman and Company, 2008.
Technology:
o All students will use a TI-83/TI-83+/TI-84 graphing calculator for all
work required.
o ALEKS Instructional Modules will be used to reinforce concepts
o Study Island will be used for AP exam practice
Student Communication Skills:
Students will be required to use statistics to evaluate and analyze real-world
situations both through textbook problems and practice AP type problems. They will
express these results through written expression, oral expression and through
technology (project).
The following outline contains the course objectives as described by The College
Board coupled with the corresponding chapter that covers the objectives.
Preliminary Chapter: What Is Statistics?
Introduction
Data Production: Where Do You Get Good Data?
Data Analysis: Making Sense of Data
Probability: What are the Chances?
Statistical Inference: Drawing Conclusions from Data
Statistical Thinking and You
HW: Handouts
Objective I A: Constructing and interpreting graphical displays of distributions of univariate data
(dotplot, stemplot, histogram, cumulative frequency plot): 1. Center and spread 2. Clusters and gaps
3. Outliers and other unusual features 4. Shape
Objective I B: Summarizing distributions of univariate data: 1. Measuring center: median, mean
2. Measuring spread: range, interquartile range, standard deviation 3. Measuring position:
quartiles, percentiles, standardized scores (z scores) 4. Using boxplots 5. The effect of changing
units on summary measures
Objective I C: Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel
boxplots) 1. Comparing center and spread: within group, between group variation 2. Comparing
clusters and gaps 3. Comparing outliers and other unusual features 4. Comparing shapes
Chapter 1: Exploring Data
(2.5 Weeks)
1.1 Displaying Distributions with Graphs
Variables: Categorical and quantitative
Dotplots and histograms
Interpreting histograms
Outliers
Center, Shape and Spread
Symmetric and skewed distributions
Stemplots
Time Plots
1.2 Describing Distributions with Numbers
Measuring Center: the mean
Measuring Center: the median
Comparing the mean and the median
Measuring Spread: the quartiles (IQR and outliers)
The five-number summary and boxplots (modified boxplots)
Measuring Spread: the standard deviation
ALEKS Instructional Modules:
Objective I A: STAT717: Interpreting Relative Frequency Histograms
STAT718: Cumulative Distributions and Ogives
STAT702: Histograms for grouped data
STAT703: Frequency Polygons for grouped data
STAT164: Comparing Means without calculation
STAT165: Comparing Standard Deviations without calculation
Objective I B: STAT023: Box-and-whisker Plots
STAT706: Mean, Median, Mode: Computations
STAT007: Weighted Mean: Tabular Data
STAT719: Estimating the mean of grouped data
STAT021: Population Standard Deviation
STAT011: Sample Standard Deviation
STAT025: Transforming the mean and standard deviation of a data set
Objective I C: STAT831: Interpreting a stem-and-leaf display
STAT827: Using back-to-back stem-and-leaf displays to compare data sets
STAT798: Mean, median, and mode: Comparisons
STAT902: Rejecting unreasonable claims based on average statistics
STAT729: Estimating the standard deviation of grouped data
HW: 3,4,6,8,11,13,14,15,25,26,29,30,31,32,33,37,39,40,42,43,45,46,56,58,66
Objective I B: Measuring position: standardized scores (z scores)
Objective III C: The Normal Distribution: 1. Properties of the normal distribution 2. Using tables of
the normal distribution 3. The normal distribution as a model for measurements
Chapter 2: The Normal Distributions
(2 Weeks)
2.1 Density Curves and the Normal Distributions
Density Curves
The median and mean of a density curve
Normal Distributions (inflection points)
The 68-95-99.7 Rule
2.2 Standard Normal Calculations
The standard normal distribution
Standardized observations
Normal distribution calculations
The standard normal table
Finding normal proportions
Finding a value given a proportion
Assessing normality (histogram, boxplot, normal probability plot)
ALEKS Instructional Modules:
Objective I B: STAT760: Standard normal values: basic
STAT160: Standard normal values: advanced
STAT009: Percentiles
Objective III C: STAT730: Empirical Rule
STAT157: Standard normal probabilities
STAT159: Normal versus standard normal density curves
STAT161: Normal distribution raw scores
STAT162: Mean and standard deviation of a normal distribution
STAT163: Normal distribution: word problems
HW: 1,2,3,4,7,8,10,12,13,14,17,19,25,26,31,32,34,35,39,50,51,59,60,61
Objective I D: Exploring bivariate data: 1. Analyzing patterns in scatterplots 2. Correlation and
linearity 3. Least-squares regression line 4. Residual plots, outliers, and influential points
Chapter 3: Examining Relationships
(2.5 Weeks)
3.1 Scatterplots
Response variable, explanatory variable
Scatterplots
Interpreting scatterplots (direction, form, strength)
Positive association, negative association
Linear relationship
Adding categorical variables to scatterplots
3.2 Correlation
The correlation r
Facts about correlation
3.3 Least-Squares Regression
Regression Line
Mathematical model
The least-squares regression line
Equation of the least-squares regression line
Facts about least-squares regression
Slope of the least-squares regression line
Coefficient of Determination
Residuals / Residual plots
Influential observations and outliers in regression
ALEKS Instructional Modules:
Objective I D: STAT339: Sketching the least-squares regression line
STAT333: Linear relationship and the sample correlation coefficient
STAT340: Predictions from the least-squares regression line
STAT930: Computing the sample correlation coefficient and the coefficients for the
least-squares regression line
STAT931: Explained and unexplained variation and the least-squares regression line
HW: 1,2,4,5,7,9,13,15,16,17,19,20,21,23,24,29,30,32,35,38,43,44,46,47,50,53,55,60,64,71,81
Objective I D: Exploring bivariate data : 5. Transformations to achieve linearity: logarithmic and
power transformations.
Objective I E: Exploring Categorical data: 1. Frequency tables and bar charts 2. Marginal and joint
frequencies for two-way tables 3. Conditional relative frequencies and association 4. Comparing
distributions using bar charts
Chapter 4: More on Two-Variable Data
(2 Weeks)
4.1 Modeling Nonlinear Data
Modeling nonlinear data
Exponential and power functions
Algebraic properties of logarithms
Exponential growth and decay
Linear growth and exponential growth
Residuals again
Power Regression
4.2 Interpreting Correlation and Regression
Extrapolation
Lurking Variables
Using averaged data
Association is not causation
Causation, common response, confounding
Associaton doesn’t imply causation
4.3 Relations in Categorical Data
Marginal Distributions
Two way tables
Describing relationships
Simpson’s Paradox
HW: 1,5,6,8,9,14,23,24,25,27,29,30,31-35,38,41-45
Objective II A: Overview of methods of data collection: 1. Census 2. Sample Survey 3.
Experiment 4. Observational Study
Objective II B: Planning and conducting surveys: 1. Characteristics of a well-designed and wellconducted survey 2. Populations, samples, and random selection 3. Sources of bias in sampling
and surveys 4. Sampling methods, including simple random sampling, stratified random sampling,
and cluster sampling
Objective II C: Planning and conducting experiments: 1. Characteristics of a well-designed and wellconducted experiment 2. Treatments, control groups, experimental units, random assignments,
and replication 3. Sources of bias and confounding, including placebo effect and blinding 4.
Completely randomized design 5. Randomized block design, including matched pairs design
Objective II D: Generalizability of results and types of conclusions that can be drawn from
observational studies, experiments, and surveys.
Chapter 5: Producing Data
(3 Weeks)
5.1 Designing Samples
Sampling
Voluntary Response Sample
Experiment
Confounding
Statistical Inference
Population, Sample
Sample design
Convenience Sampling
Bias
Simple Random Samples
Random Digits
Choosing an SRS
Probability Sample
Stratified Random Sample
Multistage Sample Design
Cautions about sample surveys
Undercoverage and Nonresponse
Response Bias
Wording of Questions
Inference about the population
5.2 Designing Experiments
Observational Study –vs- Experiment
Experimental Units, Subjects, Treatment, Factor, Level
Comparative experiments
Placebo effect
Control Group
Completely Randomized experiments
Matching
Randomization
Completely Randomized design
The Logic of Experimental Design
Statistical significance
Principles of Experimental Design: control, randomization, replication
Cautions about experimentation (hidden bias)
Double Blind experiment
Block design
Matched pairs design
5.3 Simulating Experiments
Simulation
Assigning of digits to represent outcomes
Simulate many repetitions
Simulations with calculator or computer
HW: 1,2,3,5,6,7,8,11,12,13,14,15-18,20,21,24,25,27,28,30,32,34,35,37,38,39,40,41,43,44,45,46,
47,49,5051,52,55,57,58,68
Objective III A: Probability:1. Interpreting probability, including long-run relative frequency
interpretation 2. “Law of Large Numbers” concept 3. Addition rule, multiplication rule, conditional
probability, and independence. 5. Simulation of random behavior and probability distributions
Chapter 6: Probability: The Study of Randomness (2 Weeks)
6.1 Randomness
The idea and language of probability
Randomness and probability: Random phenomenon
Thinking about randomness
The uses of probability
Independence
6.2 Probability Models
Sample Space
Tree diagram
Multiplication Principle
With and without replacement
Intuitive probability: event
Probability Rules
Complement
Disjoint
Addition Rule
Assigning probabilities: finite number of outcomes
Assigning probabilities: equally likely outcomes
Independence and the Multiplication Rule
Applying the probability rules
6.3 More About Probability
Rules of Probability: Complement, Addition, Multiplication
General Addition Rule: Union and Disjoint sets
Venn Diagrams
Conditional Probability
Joint Probability: General Multiplication Rule
Definition of Conditional Probability
Intersection
Tree Diagrams with several stages
Independent Events
ALEKS Instructional Modules:
Objective III A: STAT119: Venn diagrams: two events
STAT101: Venn diagrams: word problems
STAT106: Outcomes and event probability
STAT226: Die rolling
STAT114: Probability of intersection or union: word problems
STAT115: Independent events: basic
STAT120: Probability of union: basic
STAT104: Mutually exclusive events: two events
STAT850: Probability of independent events
STAT105: Independent events: two events
STAT851: Probability of dependent events
STAT109: Intersection and conditional probabilities
STAT107: Conditional probability: mutually exclusive events
STAT108: Conditional probability: independent events
STAT756: Tree diagrams for conditional probabilities
STAT110: Law of total probabilities
STAT113: The curious die
HW: 1,3,4,5,8,9,10,12,15,20,22,24,29,30,32,33,39,40,41,44,45,48,50,65,68,69,71,72,74,78,
82,86,87,90,98,99,101
Objective III A: 4 Discrete random variables and their probability distributions 6. Mean (expected
value) and standard deviation of a random variable, and linear transformation of a random variable
Objective III B: Combining independent random variables: 1. Notion of independence versus
dependence 2. Mean and standard deviation for sums and differences of independent random
variables
Chapter 7: Random Variables
(1.5 Weeks)
7.1 Discrete and Continuous Random Variables
Random variable
Discrete Random variable
Probability histogram
Continuous random variable
Normal distributions as probability distributions
7.2 Means and Variances of Random Variables
The mean of a random variable
Expected Value
Statistical estimation and the law of large numbers
The Law of small numbers
How large is a large number?
Rules for means
The variance of a random variable
Rules for variances
ALEKS Instructional Modules:
Objective III A and B:
STAT777: Classification of variables and levels of measurement
STAT142: Discrete versus continuous variables
STAT151: Discrete probability distribution: Basic
STAT143: Discrete probability distribution: Word problems
STAT149: Cumulative distribution function
STAT150: Expectation and variance of a random variable
STAT153: Rules for expectation and variance of random variables
STAT145: Marginal distributions of two discrete random variables
STAT146: Joint distributions of dependent or independent random variables
STAT147: Probabilities of two random variables given their joint distribution
STAT148: Conditional probabilities of two random variables given their
joint distribution
HW: 1,2,4,5,14,24,26,32,34,39,41,47,48
Mid Term Exam Chapters 1 - 7
Objective III A: 4 Discrete random variables and their probability distributions, including binomial and
geometric
Chapter 8: The Binomial and Geometric Distributions (1.5 Weeks)
8.1 The Binomial Distribution
The Binomial Setting
Binomial Distribution
Finding binomial probabilities
Cumulative distribution functions
Binomial formulas
Binomial coefficient
Binomial probability
Simulating binomial experiments
Binomial mean and standard deviation
8.2 The Geometric Distribution
The Geometric setting
Rules for calculating geometric probabilities
Exploring geometric distributions with TI-83
The expected value and other noteworthy properties of the geometric random
Variable
Probability of more than “n” trials
ALEKS Instructional Modules:
Objective III A: STAT156: Binomial problems: Mean and standard deviation
STAT174: Binomial problems: Basic
STAT155: Binomial problems: Advanced
STAT187: Normal approximation to binomial
HW: 1-5,7,10,12,13,14,15,19,21,22,25,28,31,36,38,42,49,54,58,67
Objective III D: Sampling distribution: 1. Sampling distribution of a sample proportion 2. Sampling
distribution of a sample mean 3. Central Limit Theorem 6. Simulation of Sampling Distributions
Chapter 9: Sampling Distributions
(2 Weeks)
9.1 Sampling Distributions
Parameter and Statistic
Sampling variability
Sampling distribution
Describing sampling distributions
The bias of a statistic
Unbiased statistic
The variability of a statistic
9.2 Sample Proportions
Population proportion
Sample proportion
The sampling distribution of p hat
Rule of Thumb 1
Rule of Thumb 2
9.3 Sample Means
Parameters and statistics
The mean and standard deviation of x
Sampling distribution of a sample mean
Central Limit Theorem
The Law of Large Numbers revisited
ALEKS Instructional Modules:
Objective III D: STAT185: Central Limit Theorem: Sample mean
STAT186: Central Limit Theorem: Sample sum
STAT188: Central Limit Theorem: Sample proportion
HW: 1,2,3,5,8,11,17,19,20,22,25,26,29,30,32,34,37,38,41,42,50,54
Objective IV: A: Estimation (point estimators and confidence intervals): 1. Estimating population
parameters and margins of error 2. Properties of point estimators, including unbiasedness and
variability 3. Logic of confidence intervals, meaning of confidence level and confidence intervals,
and properties of confidence intervals
Objective IV: B: Tests of significance: 1. Logic of significance testing, null and alternative
hypothesis; p-values; one- and two-sided tests; concepts of Type I and TypeII errors; concept of power.
4. Test for a mean
Chapter 10: Introduction to Inference
(3 Weeks)
10.1 Estimating with Confidence
Statistical Confidence
Confidence Interval
Margin of error
Confidence Level
Critical values
Confidence Interval for a population mean
How confidence intervals behave
Choosing the sample size for desired margin of error
Some cautions
10.2 Estimating a Population Mean
Conditions for Inference about a Population Mean
Standard Error
The t Distributions
Degrees of freedom
One-sample t confidence interval
Paired t procedures
Robustness of t procedures
10.3 Estimating a Population Proportion
Conditions for inference about a proportion
A confidence interval for a population proportion
Putting it all together: The inference toolbox
Choosing the sample size
ALEKS Instructional Modules:
Objective IV A and B:
STAT173: t distribution
STAT200: Selecting a distribution for inferences on the population mean
STAT201: Confidence interval for the population mean: use of the standard normal
STAT755: Choosing an appropriate sample size
STAT202: Confidence interval for the population mean: use of the t distribution
STAT203: Confidence interval for a population proportion
HW: 1,2,3,9,10,12,13,14,15,16,22,23,27,31,34,35,36,38,41,45,46,51,54,62,68
Objective III D: Sampling Distributions: 4. Sampling distribution of a difference between two
independent sample means 7. t-distribution
Objective IV A: Estimation: 7. Confidence interval for a difference between two means
Objective IV B: Tests of Significance: 5. Test for a difference between two means
Chapter 11: Testing a Claim (2 Weeks)
11.1 Significance Tests: The Basics
Stating the null and alternative hypotheses
Conditions for significance tests
Test statistics
P-values
Statistical significance
Interpreting Results in Context
11.2 Carrying Out Significance Tests
Z test for a population mean
Tests from confidence intervals
Confidence intervals and two-sided tests
11.3 Use and Abuse of Tests
Choosing a level of significance
Statistical significance and practical importance
Don’t ignore lack of significance
Statistical inference is not valid for all sets of data
Beware of multiple analyses
11.4 Using Inference to Make Decisions
Type I and Type II Errors
Error probabilities
Significance and Type I error
Power and Type II error
Increasing the power
ALEKS Instructional Modules:
Objective IV B: STAT300: Determining null and alternative hypothesis
STAT301: Hypothesis test for the population mean: Z test
STAT190: Type I and Type II errors
STAT192: Type I and Type II errors and power
STAT194: Effect size, sample size, and power
HW: 1,2,3,4,6,7,8,9,10,14,15,20,25,26,28,30,31,32,36,37,38,43,44,45,47,48,49,50,53,55,64
Objective III D: Sampling Distributions: 4: Sampling distribution of a difference between two
independent sample proportions
Objective IV A: Estimation: 4. Large sample confidence interval for a proportion 5. Large sample
confidence interval for a difference between two proportions
Objective IV B: Tests of Significance: 2. Large sample test for a proportion 3. Large sample test for
a difference between two proportions
Chapter 12: Significance Tests in Practice
(2 Weeks)
12.1 Tests About a Population Mean
The one-sample t statistic and the t distribution
Determining p values
The one-sample t test
More about the one-sample t test: robustness and power
12.2 Tests About a Population Proportion
The one-proportion z test
Confidence intervals provide additional information
ALEKS Instructional Modules:
Objective IV B: STAT302: Hypothesis test for the population mean: t test
STAT303: Hypothesis test for a population proportion
HW: 3,4,5,9,10,16,19,23,24,26,30,31,34,35
Chapter 13 Comparing Two Population Parameters (1 Week)
13.1 Comparing Two Means
Conditions for comparing two means
The two-sample z statistic
The two-sample t procedures
Robustness again
13.2 Comparing Two Proportions
Two-sample problems: proportions
The sampling distribution of p1 – p2
Confidence interval for comparing two proportions
Significance tests for p1 – p2
Significance test for comparing two proportions
ALEKS Instructional Modules:
Objective IV A and B:
STAT305: Hypothesis test for the difference of population means: Z test
STAT309: Hypothesis test for the difference of population means: paired
comparisons
STAT306: Hypothesis test for the difference of population means: t test
STAT307: Hypothesis test for the difference of population proportions
STAT205: Confidence interval for the difference of population means:
Use of the standard normal
STAT206: Confidence interval for the difference of population means:
Use of the t distribution
STAT207: Confidence interval for the difference of population proportions
HW: 1,2,3,5,7,8,13,14,16,18,19,23,24,26,27,29,30,33,34,38,39,44
Objective III D: Sampling Distributions: 8. Chi-Square Distribution
Objective IV B: Tests of Significance: 6. Chi-Square test for goodness of fit, homogeneity of
proportions, and independence(one- and two-way tables)
Chapter 14: Inference for Distributions of Categorical Variables: ChiSquare Procedures (1 Week)
14.1 Test for Goodness of Fit
Chi square
One-way table
Expected count
The Chi-Square goodness of fit test
Properties of the Chi-Square distributions
14.2 Inference for Two-Way Tables
Conditional distributions
The problem of multiple comparisons
Two-way tables
Stating Hypotheses
Computing Expected Cell Counts
The X2 test for homogeneity of populations
The X2 statistic and its p-value
The X2 test of association/independence
ALEKS Instructional Modules:
Objective IV B: STAT320: Chi-square goodness-of-fit test
STAT321: Chi-square test of independence
STAT319: Contingency tables: Expected frequencies
HW: 3,8,10,11,18,22,23,28,35,36,41
Objective IV A: Estimation: 8. Confidence interval for the slope of a least squares regression line
Objective IV B: Tests of Significance: 7. Test for the slope of a least squares regression line
Chapter 15: Inference for Regression (1 Week)
The regression model
Conditions for the regression model
Checking the regression conditions
Estimating the parameters
Confidence intervals for the regression slope
Testing the hypothesis of no linear relationship
ALEKS Instructional Modules:
Objective IV A and B:
STAT947: Hypothesis test for the correlation coefficient and the slope of the
Least-squares regression line
STAT325: Confidence intervals and prediction intervals from simple linear
regression
HW: 2,4,5,6,8,12,13,26
Practice Final Exam Chapters 1 – 15
2nd Semester Project:
After the AP exam is completed, students will design their own hypothesis test. They will
determine the null and alternative hypothesis, decide the sampling method and perform the
experiment. Examples of types of questions the students can ask:
 Is gender independent of choice of color of M & M?
 Does a bag of skittles match the proportion of colors that are supposed to
be in the bag?
 Is gender related to horsepower and model of a car?
 Is age related to Piaget type questions? (which glass is more full? Which
line is longer?)
 Are the ACT scores of the senior class higher than the state average?
Students will submit a design for approval, as well as the method of data collection. A written
analysis, including the positive and negatives of the project, will also be required. Students will also
submit an imovie , power point presentation, or a podcast displaying the results in a graphical
manner.