AP Statistics Course Outline
Mrs. Noonan - Columbia High School
Unit 1 – Exploring and understanding data (20 class days)
Primary materials: Stats: Modeling the Real World: Chapters 1-6
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Types of data
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TI tip: Entering data and working with data lists
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Frequency tables, pie charts, bar graphs and contingency tables,
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Histograms and relative frequency histograms, box plots, dot plots, stem and leaf or back-toback stem and leaf charts, cumulative frequency graphs, and ogives
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TI tip: Creating a histogram or box plot
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Analyzing data and graphs using GSOCS (gaps/clusters, shape, outliers, center and spread)
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Calculating and interpreting data using the five-number summary
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TI tip: Finding the five number summary
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Comparing distributions
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TI tip: comparing box plots
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Re-expressing data introduction
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Standard deviation
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(Re-scaling data)
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z-scores and percentiles, the empirical rule
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TI tip: finding normal percentages and cut points
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(normal probability plots)
Unit 2 – Exploring relationships between variables (23 class days)
Primary materials: Stats: Modeling the Real World: Chapters 7-10
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Scatter plots and correlation, (LSD)
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Explanatory and response variables
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Linear regression, least squares regression line (LSRL) and its properties
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High correlation does not imply causation
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TI tip: Making a scatter plot and finding the LSRS
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Straightening a scatter plot
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Slope of the regression line in real units
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residuals and residual plots, how to interpret a residual plot
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TI tip: making a residual plot
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How to find and interpret variation (r2 )
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(residual standard deviation)
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Outliers and influence points (leverage)
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(lurking variables)
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Straightening a curve
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(ladder of powers)
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Using logarithms to straighten a curve
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Extrapolation vs. interpolation
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TI tip: straightening a curve by re-expressing data
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Reading generic computer outputs
Unit 3- Gathering data (15 class days)
Primary materials: Stats: Modeling the Real World: Chapters 11-13
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Randomness
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The importance of sample size
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Conducting a simulation, components of a simulation
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TI tip: Using the random number generator
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Bias in surveys, types of bias
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Sample Size and census
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Population parameters
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Types of sampling: SRS, convenience, stratified, cluster and multistage, systematic
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What makes for a valid survey
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Observational studies vs. randomized, controlled experiments
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The four principles of experimental design (Control, randomize, replicate, block)
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Controls, blinding, and placebos
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Blocking
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Matched pairs
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Factors/levels/treatments
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Confounding (and lurking) variables
Project: Data Collection and Analysis (4 class days)
Unit 4- Randomness and Probability (17 class days)
Primary materials: Stats: Modeling the Real World: Chapters 14-17
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The law of large numbers
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The non-existent law of averages
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Basic probability rules and concepts
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Mutually exclusive events,
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Independent events
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Venn diagrams
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With/without replacement
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Addition and multiplication rules
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Conditional probabilities
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Tree diagrams
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Reverse conditioning
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Random variables and expected value
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Means and variances of random variables
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Why variances add but standard deviations don’t
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Continuous vs. discrete random variables and the normal curve
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Area under the curve = probability concept
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The geometric model for probability
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Four requirements of a geometric setting
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The Binomial model
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Four requirements of a binomial setting
Unit 5- Sampling Distributions and Statistical Inference for Proportions (17 class days)
Primary materials: Stats: Modeling the Real World: Chapters 18-22
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Introduction to statistical inference
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The Central Limit Theorem for sample proportions
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Assumptions and conditions
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Sampling distribution model for a proportion
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Sampling distribution for a mean
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About variation
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Finding a confidence interval for a proportion
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Relating proportions to a binomial setting/distribution
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When n is large enough, assume normalcy reading a Z table
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Interpretation of “95% confidence”
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Margin of error
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Critical values for z-scores
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Assumptions and conditions
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Determining a minimum sample size for a given margin of error
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Interpreting a confidence interval
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Introduction to hypothesis tests
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P-values –interpretation
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Hypothesis tests and HAMC (hypothesis, assumptions/conditions, mechanics, conclusion in
context)
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One and two tailed tests
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TI tip: 1 proportion z-test
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Alpha levels
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Significant vs. important
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Confidence Intervals and hypothesis tests – how these two tests can “tell” us the same
information
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Type I and Type II errors
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Power of the test
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Comparing two proportions
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Standard deviation of a difference
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The sampling distribution of the difference of means
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Finding a two-proportion z-interval
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Finding Ho for the difference of two proportions
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Two-proportion z-test
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TI tip: two proportion z-tests and confidence intervals
Unit 6- Inferences about Means (11 class days)
Primary materials: Stats: Modeling the Real World: Chapters 23-25
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T distributions – family of curves
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Reading a t-table vs. a z-table
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Degrees of freedom
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ZAPTAX (Mr. T is always mean – Z table Always for Proportions, T table Always for Means)
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One sample T statistic
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Confidence interval for means
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TI tip: finding t-model probabilities and cut scores
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Assumptions and conditions – sample size and normalcy
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TI tip: testing a hypothesis about a mean
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Comparing two means (difference of)
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TI tip: testing a difference of means
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Reading generic computer output
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Paired samples and blocks
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Group Project
Unit 7- Inference When Variables Are Related (9 class days)
Primary materials: Stats: Modeling the Real World: Chapters 26-27
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The Goodness of Fit test (GOF)
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The Chi-square statistic and degrees of freedom
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Reading/interpreting the Chi-square table
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TI tip – goodness of fit on the calculator
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Two-way tables and Chi-square formulas
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Assumptions and conditions
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Chi-square Tests for Homogeneity and Independence
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Calculating expected counts
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Importance of sample size/ expected count size
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(Examining the residuals)
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Introduction to inferences for regression lines
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Review of scatter plots
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Assumptions and conditions for inference for regression
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T-test for the slope of the regression line
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Reading/ interpreting generic computer outputs
Unit 8: Review for AP Statistics Exam ( 10-15 class days as schedule permits)
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Complete the 2007 AP Exam in class over the course of four class days
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Analyze results
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Review major concepts/ themes of course
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Review calculator usage
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Exam strategies/tips
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Preparing for the AP Statistics Exam
Total class days: 126