Download AP Statistics Course of Study

AP Statistics Course of Study
This course of study follows the description set out by CollegeBoard in their AP
Statistics course description. It uses the textbook The Practice of Statistics, 3rd
edition by Yates, Moore, and Starnes; as well as much of the supplemental
material provided to teachers by W.H. Freeman, the book’s publisher.
The purpose of this course is to introduce students to the major concepts and
tools for collecting, analyzing, and drawing conclusions from data. After
describing each conceptual theme, the portions of the YMS book that correspond
to that theme will be detailed.
Following the thematic description, this document will go through the book
chapter by chapter. First, the major ideas from each chapter will be grouped.
Then, each and every learning target from each chapter will be listed by chapter
section.
AP Statistics Course of Study
Page 1 of 1
Students in this course will be exposed to four broad conceptual
themes:
Exploring Data: Describing patterns and departures from patterns
(20%–30%) Exploratory analysis of data makes use of graphical and
numerical techniques to study patterns and departures from patterns.
Emphasis will be placed on interpreting information from graphical
and numerical displays and summaries. This theme is covered in
Chapters 1-4 of this course.
Sampling and Experimentation: Planning and conducting a study
(10%–15%) Data must be collected according to a well-developed plan
if valid information on a conjecture is to be obtained. This plan
includes clarifying the question and deciding upon a method of data
collection and analysis. This theme is covered in Chapter 5 of this
course; ideas regarding planning and conducting a study are
presented in Chapter 4 as well.
Anticipating Patterns: Exploring random phenomena using
probability and simulation (20%–30%) Probability is the tool used
for anticipating what the distribution of data should look like under a
given model. This theme is covered primarily in Chapters 7-9 of this
course; the t distribution is covered in Chapter 10.
Statistical Inference: Estimating population parameters and testing
hypotheses (30%–40%) Statistical inference guides the selection of
appropriate models. This theme is covered in Chapters 10-15 of this
course.
AP Statistics Course of Study
Page 2 of 2
Chapter One: Exploring Data
Use a variety of graphical techniques to display a distribution. These
will include bar graphs, pie charts, stemplots, histograms, ogives,
time plots, and boxplots.
Interpret graphical displays in terms of the shape, center, and spread
of the distribution, as well as gaps and outliers.
Use a variety of numerical techniques to describe a distribution.
These will include mean, median, quartiles, five-number summary,
interquartile range, standard deviation, range, and variance.
Interpret numerical measures in the context of the situation in which
they occur.
Learn to identify outliers in a data set.
Explore the effects of a linear transformation of a data set.
Section 1.1: Displaying Distributions with Graphs
Describe what is meant by exploratory data analysis.
Explain what is meant by the distribution of a variable.
Differentiate between categorical variables and quantitative
variables.
Construct bar graphs and pie charts for a set of categorical data.
Construct a stemplot for a set of quantitative data.
Construct a back-to-back stemplot to compare two related
distributions.
Construct a stemplot using split stems.
AP Statistics Course of Study
Page 3 of 3
Construct a histogram for a set of quantitative data, and discuss how
changing the class width can change the impression of the data given
by the histogram.
Describe the overall pattern of a distribution by its shape, center, and
spread.
Explain what is meant by the mode of a distribution.
Recognize and identify symmetric and skewed distributions.
Explain what is meant by an outlier in a stemplot or histogram.
Construct and interpret an ogive (relative cumulative frequency
graph) from a relative frequency table.
Construct a time plot for a set of data collected over time.
Section 1.2: Describing Distributions with Numbers
Given a data set, compute the mean and median as measures of
center.
Explain what is meant by a resistant measure.
Identify situations in which the mean is the most appropriate
measure of center and situations in which the median is the most
appropriate measure.
Given a data set, find the quartiles.
Given a data set, find the five-number summary.
Use the five-number summary of a data set to construct a boxplot for
the data.
Compute the interquartile range (IQR) of a data set.
Given a data set, use the 1.5 × IQR rule to identify outliers.
AP Statistics Course of Study
Page 4 of 4
Given a data set, compute the standard deviation and variance as
measures of spread.
Give two reasons why we use squared deviations rather than just
average deviations from the mean.
Explain what is meant by degrees of freedom.
Identify situations in which the standard deviation is the most
appropriate measure of spread and situations in which the
interquartile range is the most appropriate measure.
Explain the effect of a linear transformation of a data set on the
mean, median, and standard deviation of the set.
Use numerical and graphical techniques to compare two or more data
sets.
Chapter Two: Describing Location in a Distribution
Be able to compute measures of relative standing for individual values
in a distribution. This includes standardized values (z-scores) and
percentile ranks.
Use Chebyshev’s inequality to describe the percentage of values in a
distribution within an interval centered at the mean.
Demonstrate an understanding of a density curve, including its mean
and median.
Demonstrate and understanding of the Normal distribution and the
68-95-99.7 Rule.
Use tables and technology to find (a) the proportion of values on an
interval of the Normal distribution and (b) a value with a given
proportion of observations above or below it.
Use a variety of techniques, including construction of a normal
probability plot, to assess the Normality of a distribution.
Section 2.1: Measures of Relative Standing and Density Curves
AP Statistics Course of Study
Page 5 of 5
Explain what is meant by a standardized value.
Compute the z-score of an observation given the mean and standard
deviation of a distribution.
Compute the pth percentile of an observation.
Define Chebyshev’s inequality, and give an example of its use.
Explain what is meant by a mathematical model.
Define a density curve.
Explain where the mean and median of a density curve are to be
found.
Describe the relative position of the mean and median in a symmetric
density curve and in a skewed density curve.
Section 2.2: Normal Distributions
Identify the main properties of the Normal curve as a particular
density curve.
List three reasons why Normal distributions are important in
statistics.
Explain the 68-95-99.7 rule (the empirical rule).
Explain the notation N(  ,  ).
Define the standard Normal distribution.
Use a table of values for the standard Normal curve to compute the
proportion of observations that are (a) less than a given z-score, (b)
greater than a given z-score, or (c) between two given z-scores.
Use a table of values for the standard Normal curve to find the
proportion of observations in any region given any Normal
distribution (i.e., given raw data rather than z-scores).
AP Statistics Course of Study
Page 6 of 6
Use a table of values for the standard Normal curve to find a value
with a given proportion of observations above or below it (inverse
Normal).
Identify at least two graphical techniques for assessing Normality.
Explain what is meant by a Normal probability plot; use it to help
assess the Normality of a given data set.
Use technology to perform Normal distribution calculations and to
make Normal probability plots.
Chapter Three: Examining Relationships
Construct and interpret a scatterplot for a set of bivariate data.
Compute and interpret the correlation r between two variables.
Demonstrate an understanding of the basic properties of the
correlation r.
Explain the meaning of a least squares regression line.
Given a bivariate data set, construct and interpret a regression line.
Demonstrate an understanding of how one measures the quality of a
regression line as a model for bivariate data.
Section 3.1: Scatterplots and Correlation
Explain the difference between an explanatory variable and a
response variable.
Given a set of bivariate data, construct a scatterplot.
Explain what is meant by the direction, form, and strength of the
overall pattern of a scatterplot.
Explain how to recognize an outlier in a scatterplot.
AP Statistics Course of Study
Page 7 of 7
Explain what it means for two variables to be positively or negatively
associated.
Explain how to add categorical variables to a scatterplot.
Use a graphing calculator to construct a scatterplot. {Construct a
scatterplot by hand.} {Construct a scatterplot using computer
software.}
Define the correlation r and describe what it measures.
Given a set of bivariate data, use technology to compute the
correlation r. {Manually compute r for a small data set.}
List the four basic properties of the correlation r that you need to
know to interpret any correlation.
List four other facts about correlation that must be kept in mind when
using r.
Section 3.2: Least-Squares Regression
Explain what is meant by a regression line.
Given a regression equation, interpret the slope and y-intercept in
context.
Explain what is meant by extrapolation.
Explain why the regression line is called the “least-squares regression
line” (LSRL)
Explain how the coefficients of the regression equation, ŷ  a  bx , can
be found given r, sx, sy, and (x, y) .
Given a bivariate data set, use technology to construct a least-squares
regression line. {Manually construct a least-squares regression line
for a small data set.}
Define a residual.
AP Statistics Course of Study
Page 8 of 8
Given a bivariate data set, use technology to construct a residual plot
for a linear regression.
List two things to consider about a residual plot when checking to see
if a straight line is a good model for a bivariate data set.
Explain what is meant by the standard deviation of the residuals.
Define the coefficient of determination, r2, and explain how it is used
in determining how well a linear model fits a bivariate set of data.
List and explain four important facts about least-squares regression.
Section 3.3: Correlation and Regression Wisdom
Recall the three limitations on the use of correlation and regression.
Explain what is meant by an outlier in bivariate data.
Explain what is meant by an influential observation and how it relates
to regression.
Given a scatterplot in a regression setting, identify outliers and
influential observations.
Define a lurking variable.
Give an example of what it means to say “association does not imply
causation.”
Explain how correlations based on averages differ from correlations
based on individuals.
Chapter Four: More about Relationships between Two
Variables
Identify settings in which a transformation might be necessary to
achieve linearity.
AP Statistics Course of Study
Page 9 of 9
Use transformations involving powers and logarithms to linearize
curved relationships.
Explain what is meant by a two-way table, and describe its parts.
Give an example of Simpson’s paradox.
Explain what gives the best evidence for causation.
Explain the criteria for establishing causation when experimentation
is not feasible.
Section 4.1: Transforming to Achieve Linearity
Explain what is meant by transforming (re-expressing) data.
Discuss the advantages of transforming nonlinear data.
Tell where y  log(x) fits into the hierarchy of power transformations.
Explain the ladder of power transformations.
Explain how linear growth differs from exponential growth.
Identify real-life situations in which a transformation can be used to
linearize data from an exponential growth model.
Use a logarithmic transformation to linearize a data set that can be
modeled by an exponential model.
Identify situations in which a transformation is required to linearize a
power model.
Use a transformation to linearize a data set that can be modeled by a
power model.
Section 4.2: Relationships between Categorical Variables
Explain what is meant by a two-way table.
Explain what is meant by marginal distributions in a two-way table.
AP Statistics Course of Study
Page 10 of 10
Describe how changing counts to percents is helpful in describing
relationships between categorical variables.
Explain what is meant by a conditional distribution.
Define Simpson’s paradox, and give an example of it.
Section 4.3: Establishing Causation
Identify the three ways in which the association between two
variables can be explained.
Explain what process provides the best evidence for causation.
Define what is meant by a common response.
Define what it means to say that two variables are confounded.
Discuss why establishing a cause-and-effect relationship through
experimentation is not always possible.
Explain what it means to say that a lack of evidence for cause-andeffect relationship does not necessarily mean that there is no causeand-effect relationship.
List five criteria for establishing causation when you cannot conduct
a controlled experiment.
AP Statistics Course of Study
Page 11 of 11
Chapter Five: Producing Data
Distinguish between, and discuss the advantages of, observational
studies and experiments.
Identify and give examples of different types of sampling methods,
including a clear definition of a simple random sample.
Identify and give examples of sources of bias in sample surveys.
Identify and explain the three basic principles of experimental
design.
Explain what is meant by a completely randomized design.
Distinguish between the purposes of randomization and blocking in
an experimental design.
Use random numbers from a table or technology to select a random
sample.
Section 5.1: Designing Samples
Define population and sample.
Explain how sampling differs from census.
Explain what is meant by a voluntary response sample.
Give an example of a voluntary response sample.
Explain what is meant by convenience sampling.
Define what it means for a sampling method to be biased.
Define, carefully, a simple random sample (SRS).
List the four stems involved in choosing an SRS.
Explain what is meant by systematic random sampling.
AP Statistics Course of Study
Page 12 of 12
Use a table of random digits to select a simple random sample.
Define a probability sample.
Given a population, determine the strata of interest, and select a
stratified random sample.
Define a cluster sample.
Define undercoverage and nonresponse as sources of bias in sample
surveys.
Give an example of response bias in a survey question.
Write a survey question in which the wording of the question is likely
to influence the response.
Identify the major advantage of large random samples.
Section 5.2: Designing Experiments
Define experimental units, subjects, and treatment.
Define factor and level.
Given a number of factors and the number of levels for each factor,
determine the number of treatments.
Explain the major advantage of an experiment over an observational
study.
Give an example of the placebo effect.
Explain the purpose of a control group.
Explain the difference between control and a control group.
Discuss the purpose of replication, and give an example of replication
in the design of an experiment.
Discuss the purpose of randomization in the design of an experiment.
AP Statistics Course of Study
Page 13 of 13
Given a list of subjects, use a table of random numbers to assign
individuals to treatment and control groups.
List the three main principles of experimental design.
Explain what it means to say that an observed effect is statistically
significant.
Define a completely randomized design.
For an experiment, generate an outline of a completely randomized
design.
Define a block.
Give an example of block design in an experiment.
Explain how block design may be better than a completely
randomized design.
Give an example of matched pairs design, and explain why matched
pairs are an example of block designs.
Explain what is meant by a study being double blind.
Give an example in which a lack of realism negatively affects our
ability to generalize the results of a study.
AP Statistics Course of Study
Page 14 of 14
Chapter Six: Probability and Simulation – The Study of
Randomness
Perform a simulation of probability problem using a table of random
numbers or technology.
Use the basic rules of probability to solve probability problems.
Write out the sample space for a probability random phenomenon,
and use it to answer probability questions.
Describe what is meant by the intersection and union of two events.
Discuss the concept of independence.
Use general addition and multiplication rules to solve probability
problems.
Solve problems involving conditional probability, using Bayes’s rule
when appropriate.
Section 6.1: Simulation
Define simulation.
List the five steps involved in a simulation.
Explain what is meant by independent trials.
Use a table of random digits to carry out a simulation.
Given a probability problem, conduct a simulation in order to
estimate the probability desired.
Use a calculator or computer to conduct a simulation of a probability
problem.
AP Statistics Course of Study
Page 15 of 15
Section 6.2: Probability Models
Explain how the behavior of a chance event differs in the short-run
and long-run.
Explain what is meant by a random phenomenon.
Explain what it means to say that the idea of probability is empirical.
Define probability in terms of relative frequency.
Define sample space.
Define event.
Explain what is meant by a probability model.
Construct a tree diagram.
Use the multiplication principle to determine the number of
outcomes in a sample space.
Explain what is meant by sampling with replacement and sampling
without replacement.
List the four rules that must be true for any assignment of probability.
Explain what is meant by {A  B} and {A  B} .
Explain what is meant by each of the regions in a Venn diagram.
Give an example of two events A and B where A  B   .
Use a Venn diagram to illustrate the intersection of two events A and
B.
Compute the probability of an event given the probabilities of the
outcomes that make up the event.
Explain what is meant by equally likely outcomes.
AP Statistics Course of Study
Page 16 of 16
Compute the probability of an event in the special case of equally
likely outcomes.
Define what it means for two events to be independent.
Give the multiplication rule for independent events.
Given two events, determine if they are independent.
Section 6.3 General Probability Rules
State the addition rule for disjoint events.
State the general addition rule for union of two events.
Given any two events A and B, compute P(A  B) .
Define what is meant by a joint event and joint probability.
Explain what is meant by the conditional probability P(B | A) .
State the general multiplication rule for any two events.
Use the general multiplication rule to define P(B | A) .
Explain what is meant by Bayes’s rule.
Define independent events in terms of a conditional probability.
Chapter Seven: Random Variables
Define what is meant by a random variable.
Define a discrete random variable.
Define a continuous random variable.
Explain what is meant by the probability distribution for a random
variable.
Explain what is meant by the law of large numbers.
AP Statistics Course of Study
Page 17 of 17
Calculate the mean and variance of a discrete random variable.
Calculate the mean and variance of distributions formed by
combining two random variables.
Section 7.1: Discrete and Continuous Random Variables
Define a discrete random variable.
Explain what is meant by a probability distribution.
Construct the probability distribution for a discrete random
variable.
Given a probability distribution for a discrete random variable,
construct a probability histogram.
Review: define a density curve.
Explain what is meant by a uniform distribution.
Define a continuous random variable and probability distribution
for a continuous random variable.
Section 7.2: Means and Variances of Random Variables
Define what is meant by the mean of a random variable.
Calculate the mean of a discrete random variable.
Calculate the variance and standard deviation of a discrete random
variable.
Explain, and illustrate with an example, what is meant by the law of
large numbers.
Explain what is meant by the law of small numbers.
Given  X and Y , calculate a bX , and  X Y .
AP Statistics Course of Study
Page 18 of 18
Given  X and  Y , calculate  2a bX and  2X Y (where X and Y are
independent).
Explain how standard deviations are calculated when combining
random variables.
Discuss the shape of linear combination of independent Normal
random variables.
Chapter Eight: The Binomial and Geometric Distributions
Explain what is meant by a binomial setting and binomial
distribution.
Use technology to solve probability questions in a binomial setting.
Calculate the mean and variance of a binomial random variable.
Solve a binomial probability problem using a Normal approximation.
Explain what is meant by a geometric setting.
Solve probability questions in a geometric setting.
Calculate the mean and variance of a geometric random variable.
Section 8.1: The Binomial Distributions
Describe the conditions that need to be present to have a binomial
setting.
Define a binomial distribution.
Explain when it might be all right to assume a binomial setting even
though the independence condition is not satisfied.
Explain what is meant by the sampling distribution of a count.
State the mathematical expression that gives the value of a binomial
coefficient. Explain how to find the value of that expression.
AP Statistics Course of Study
Page 19 of 19
State the mathematical expression used to calculate the value of
binomial probability.
Evaluate a binomial probability by using the mathematical formula
for P(X  k) .
Explain the difference between binompdf(n,p,X) and
binomcdf(n,p,X).
Use your calculator to help evaluate a binomial probability.
If X is B(n, p) , find  X and  X (that is, calculate the mean and variance
of a binomial distribution).
Use a Normal approximation for a binomial distribution to solve
questions involving binomial probability.
Section 8.2: The Geometric Distributions
Describe what is meant by a geometric setting.
Given the probability of success, p, calculate the probability of getting
the first success on the nth trial.
Calculate the mean (expected value) and the variance of a geometric
random variable.
Calculate the probability that it takes more than n trials to see the
first success for a geometric random variable.
Use simulation to solve geometric probability problems.
Chapter Nine: Sampling Distributions
Define a sampling distribution.
Contrast bias and variability.
Describe the sampling distribution of a sample proportion (shape,
center, and spread).
AP Statistics Course of Study
Page 20 of 20
Use a Normal approximation to solve probability problems involving
the sampling distribution of a sample proportion.
Describe the sampling distribution of a sample mean.
State the central limit theorem.
Solve probability problems involving the sampling distribution of a
sample mean.
Section 9.1: Sampling Distributions
Compare and contrast parameter and statistic.
Explain what is meant by sampling variability.
Define the sampling distribution of a statistic.
Explain how to describe a sampling distribution.
Define an unbiased statistic and an unbiased estimator.
Describe what is meant by the variability of a statistic.
Explain how bias and variability are related to estimating with a
sample.
Section 9.2: Sample Proportions
Describe the sampling distribution of a sample proportion.
(Remember: “describe” means tell about shape, center, and spread.)
Compute the mean and standard deviation for the sampling
distribution of p̂ .
Identify the “rule of thumb” that justifies the use of the recipe for the
standard deviation of p̂ .
Identify the conditions necessary to use a Normal approximation to
the sampling distribution of p̂ .
AP Statistics Course of Study
Page 21 of 21
Use a Normal approximation to the sampling distribution of p̂ to
solve probability problems involving p̂ .
Section 9.3: Sample Means
Given the mean and standard deviation of a population, calculate the
mean and standard deviation for the sampling distribution of a
sample mean.
Identify the shape of the sampling distribution of a sample mean
drawn from a population that has a Normal distribution.
State the central limit theorem.
Use the central limit theorem to solve probability problems for the
sampling distribution of a sample mean.
AP Statistics Course of Study
Page 22 of 22
Chapter Ten: Estimating with Confidence
Describe statistical inference.
Describe the basic form of all confidence intervals.
Construct and interpret a confidence interval for a population mean
(including paired data) and for a population proportion.
Describe a margin of error, and explain ways in which you can
control the size of the margin of error.
Determine the sample size necessary to construct a confidence
interval for a fixed margin of error.
Compare and contrast the t distribution and the Normal distribution.
List the conditions that must be present to construct a confidence
interval for a population mean or a population proportion.
Explain what is meant by the standard error, and determine the
standard error of x and the standard error of p̂ .
Section 10.1: Confidence Intervals – The Basics
List the (six) basic steps in the reasoning of statistical estimation.
Distinguish between a point estimate and an interval estimate.
Identify the basic form of all confidence intervals.
Explain what is meant by margin of error.
State in nontechnical language what is meant by a “level C confidence
interval.”
State the three conditions that need to be present in order to
construct a valid confidence interval.
AP Statistics Course of Study
Page 23 of 23
Explain what it means by the “upper p critical value” of the standard
Normal distribution.
For a known population standard deviation  , construct a level C
confidence interval for a population mean.
List the four necessary steps in the creation of a confidence interval
(see Inference Toolbox).
Identify three ways to make the margin of error smaller when
constructing a confidence interval.
Once a confidence interval has been constructed for a population
value, interpret the interval in the context of the problem.
Determine the sample size necessary to construct a level C confidence
interval for a population mean with a specified margin of error.
Identify as many of the six “warnings” about constructing confidence
intervals as you can. (For example, a nice formula cannot correct for
bad data.)
Section 10.2: Estimating a Population Mean
Identify the three conditions that must be present before estimating a
population mean.
Explain what is meant by the standard error of a statistic in general
and by the standard error of the sample mean in particular.
List three important facts about the t distributions. Include
comparisons to the standard Normal curve.
Use Table C to determine critical t value for a given level C
confidence interval for a mean and a specified number of degrees of
freedom.
Construct a one-sample t confidence interval for a population mean
(remembering to use the four-step procedure).
Describe what is meant by paired t procedures.
AP Statistics Course of Study
Page 24 of 24
Calculate a level C t confidence interval for a set of paired data.
Explain what is meant by a robust inference procedure and comment
on the robustness of t procedures.
Discuss how sample size affects the usefulness of t procedures.
Section 10.3: Estimating a Population Proportion
Given a sample proportion, p̂ , determine the standard error of p̂ .
List the three conditions that must be present before constructing a
confidence interval for an unknown population proportion.
Construct a confidence interval for a population proportion,
remembering to use the four-step procedure (see the Inference
Toolbox).
Determine the sample size necessary to construct a level C confidence
interval for a population proportion with a specified margin of error.
Chapter Eleven: Testing a Claim
Explain the logic of significance testing.
List and explain the difference between a null hypothesis and an
alternative hypothesis.
Discuss the meaning of statistical significance.
Use the Inference Toolbox to conduct a large sample test for a
population mean.
Compare two-sided significance tests and confidence intervals when
doing inference.
Differentiate between statistical and practical “significance.”
Explain, and distinguish between, two types of errors in hypothesis
testing.
AP Statistics Course of Study
Page 25 of 25
Define and discuss the power of a test.
Section 11.1: Significance Tests – The Basics
Explain why significance testing looks for evidence against a claim
rather than in favor of the claim.
Define null hypothesis and alternative hypothesis.
Explain the difference between a one-sided hypothesis and a twosided hypothesis.
Identify the three conditions that need to be present before doing a
significance test for a mean
Explain what is meant by a test statistic. Give the general form of a
test statistic.
Define P-value.
Define significance level.
Define statistical significance (statistical significance at level  ).
Explain the difference between the P-value approach to significance
testing and the statistical significance approach.
Section 11.2: Carrying Out Significance Tests
Identify and explain the four steps involved in formal hypothesis
testing.
Using the Inference Toolbox, conduct a z test for a population mean.
Explain the relationship between a level  two-sided significance test
for  and a level 1   confidence interval for  .
Conduct a two-sided significance test for  using a confidence
interval.
Section 11.3: Use and Abuse of Tests
AP Statistics Course of Study
Page 26 of 26
Distinguish between statistical significance and practical
importance.
Identify the advantages and disadvantages of using P-values rather
than a fixed level of significance.
Section 11.4: Using Inference to Make Decisions
Define what is meant by a Type I error.
Define what is meant by a Type II error.
Describe, given a real situation, what constitutes a Type I error and
what the consequences of such an error would be.
Describe, given a real situation, what constitutes a Type II error and
what the consequences of such an error would be.
Describe the relationship between significance level and a Type I
error.
Define what is meant by the power of a test.
Identify the relationship between the power of a test and a Type II
error.
List four ways to increase the power of a test.
Explain why a large value for the power of a test is desirable.
Chapter Twelve: Significance Tests in Practice
Conduct one-sample and paired data t significance tests.
Explain the difference between the one-sample confidence interval
for a population proportion and the one-sample significance test for a
population proportion.
Conduct a significance test for a population proportion.
Section 12.1: Tests about a Population Mean
AP Statistics Course of Study
Page 27 of 27
Define the one-sample t statistic.
Determine the critical values of t(t*), from a “t table” given the
probability of being to the right or left of t*.
Determine the P-value of a t statistic for both a one- and two-sided
significance test.
Conduct a one-sample t significance test for a population mean using
the Inference Toolbox.
Conduct a paired t test for the difference between two population
means.
Section 12.2: Tests about a Population Proportion
Explain why p0 , rather than p̂ is used when computing the standard
error of p̂ in a significance test for a population proportion.
Explain why the correspondence between a two-tailed significance
test and a confidence interval for a population proportion is not as
exact as when testing for a population mean.
Explain why the test for a population proportion is sometimes called
a large sample test.
Conduct a significance test for a population proportion using the
Inference Toolbox.
Discuss how significance tests and confidence intervals can be used
together to help draw conclusions about a population proportion.
Chapter Thirteen: Comparing Two Population Parameters
Identify the conditions that need to be satisfied in order to do
inference for comparing two population means.
Construct a confidence interval for the difference between two
population means.
AP Statistics Course of Study
Page 28 of 28
Perform a significance test for the difference between two population
means.
Identify the conditions that need to be satisfied in order to do
inference for comparing two population proportions.
Construct a confidence interval for the difference between two
population proportions.
Perform a significance test for the difference between two population
proportions.
Section 13.1: Comparing Two Means
Identify situations in which two-sample problems might arise.
Describe the three conditions necessary for doing inference involving
two population means.
Clarify the difference between the two-sample z statistic and the twosample t statistic.
Identify the two practical options for using two-sample t procedures
and how they differ in terms of computing the number of degrees of
freedom.
Conduct a two-sample significance test for the difference between
two independent means using the Inference Toolbox.
Compare the robustness of two-sample procedures with that of onesample procedures. Include in your comparison the role of equal
sample sizes.
Explain what is meant by “pooled two-sample t procedures,” when
pooling can be justified, and why it is advisable not to pool.
AP Statistics Course of Study
Page 29 of 29
Section 13.2: Comparing Two Proportions
Identify the mean and standard deviation of the sampling
distribution of p̂1  p̂2 .
List the conditions under which the sampling distribution of p̂1  p̂2 is
approximately Normal.
Indentify the standard error of p̂1  p̂2 when constructing a
confidence interval for the difference between two population
proportions.
Identify the three conditions under which it is appropriate to
construct a confidence interval for the difference between two
population proportions.
Construct a confidence interval for the difference between two
population proportions using the four-step Inference Toolbox for
confidence intervals.
Explain why, in a significance test for the difference between two
proportions, it is reasonable to combine (pool) your sample estimates
to make a single estimate of the difference between the proportions.
Explain how the standard error of p̂1  p̂2 differs between constructing
a confidence interval for p1  p2 and performing a hypothesis test for
H 0 : p1  p2  0 .
List the three conditions that need to be satisfied in order to do a
significance test for the difference between two proportions.
Conduct a significance test for the difference between two
proportions using the Inference Toolbox.
Chapter Fourteen: Inference for Distributions of
Categorical Variables – Chi-Square Procedures
Explain what is meant by a chi-square goodness of fit test.
AP Statistics Course of Study
Page 30 of 30
Conduct a chi-square goodness of fit test.
Given a two-way table, compute conditional distributions.
Conduct a chi-square test for homogeneity of populations.
Conduct a chi-square test for association/independence.
Use technology to conduct a chi-square significance test.
Section 14.1: Test for Goodness of Fit
Describe the situation for which the chi-square test for goodness of fit
is appropriate.
Define the  2 statistic and identify the number of degrees of freedom
it is based on, for the  2 goodness of fit test.
List the conditions that need to be satisfied in order to conduct a  2
test for goodness of fit.
Conduct a  2 test for goodness of fit.
Identify three main properties of the chi-square density curve.
Use technology to conduct a  2 test for goodness of fit.
If a  2 statistic turns out to be significant, discuss how to determine
which observations contribute the most to the total value.
Section 14.2: Inference for Two-Way Tables
Explain what is meant by a two-way table.
Given a two-way table, compute the row or column conditional
distributions.
Define the chi-square (  2 ) statistic.
AP Statistics Course of Study
Page 31 of 31
Using the words populations and categorical variables, describe the
major difference between homogeneity of populations and
independence.
Identify the form of the null hypothesis in a  2 test for homogeneity
of populations.
Identify the form of the null hypothesis in a  2 test of
association/independence.
Given a two-way table of observed counts, calculate the expected
counts for each cell.
List the conditions necessary to conduct a  2 test of significance for a
two-way table.
Use technology to conduct a  2 test of significance for a two-way
table.
Discuss techniques of determining which components contribute the
most to the value of  2 .
Describe the relationship between a  2 statistic for a two-way table
and a two-proportion z statistic.
Chapter Fifteen: Inference for Regression
Identify the conditions necessary to do inference for regression.
Given a set of data, check that the conditions for doing inference for
regression are present.
Explain what is meant by the standard error about the least-squares
line.
Compute a confidence interval for the slope of the regression line.
Conduct a test of the hypothesis that the slope of the regression line is
0 (or that the correlation is 0) in the population.
AP Statistics Course of Study
Page 32 of 32
Use of Technology
For most statistical techniques, students will perform computations
in several ways: by hand on small data sets, using handheld graphing
calculators on larger data sets, and on very large real-world datasets
using microcomputer spreadsheet and statistical-analysis software.
AP Statistics Course of Study
Page 33 of 33