Download AP Stats Syllabus

Advanced Placement Statistics – S. Walter - BCHS
Syllabus 2016
Primary Textbook: Yates, Daniel, Moore, David, and Daren Starnes. The Practice of
Statistics, fifth edition. New York: W.H. Freeman and Company, 2008.
Technology:
o All students will use a TI-84 graphing calculator for all work required.
o All students will be exposed to Minitab computer output in sample
problems and during classroom demonstration. Students will have
some assignments that require use of Minitab software or
interpretation of Minitab output.
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
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
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)
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
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
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
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
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
Mid Term Exam Chapters 1 - 7
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
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
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
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
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
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
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
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
Practice Final Exam Chapters 1 – 15
1st Semester Project: (after Chapter 5)
Students will design a survey that will explore response bias. Since we have explored
different types of bias, students will choose the type of bias that they want to confirm. A proposal of
the initial question, (how bias will be determined), how subjects will be selected and a graphical
display of the results will be required. Some examples of projects students have chosen:
 Does gender influence the response to whether girls/boys are better at sports?
(person asking question – 1 male and other female)
 Would you date a girl taller than you? (one person asking question is much taller
than other)
 Do you think cheerleaders are ditsy? (one person asking question is a cheerleader;
other person is not)
 Can wording of the question play a role in the response of the survey?
Students will submit a written analysis as well as present the projects in the form of an imovie to the
class. The class will have the opportunity to ask questions concerning what worked and what did not
work in the activity.
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.