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AP Stats Study Guide
EXPLORING DATA
P. What is statistics?
Give a definition of statistics, and describe what statistics helps you do.
Explain why anecdotal evidence is not considered valid statistical data.
Discuss the advantages of using available data, and identify at least two methods of obtaining it.
Identify the three main statistical designs for producing data.
Give an example of poorly collected data.
Explain the difference between a survey and an experiment.
Explain how an experiment differs from an observational study.
Identify the best source of data if you want to establish a cause-and-effect relationship.
Explain the difference between individuals and variables.
List and describe the four key questions you should ask about a data set.
Differentiate between categorical and quantitative variables.
Define the distribution of a variable.
Describe the basic techniques used in describing both the categorical and quantitative data.
Explain what is meant by a lurking variable.
Explain how probability helps us to decide if an observation can reasonably be attributed to
chance.
Explain how sample values are used to make inferences about a population from which a sample
was drawn. Include a discussion of variation in your response.
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1. Exploring data
Use a variety of graphical techniques to display a distribution. These should 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 should 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.
2. Describing location in a distribution
Explain what is meant by a "standardized value".
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.
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.
Demonstrate an 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.
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3. 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.
4. More about relationships between two variables
Identify settings in which a transformation might be necessary in order to achieve linearity.
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.
SAMPLING AND EXPERIMENTATION
5. 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.
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ANTICIPATING PATTERNS
6. Probability and simulation: the study of randomness
Perform a simulation of a 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.
7. Random variables
Define what is meant by a random variable.
Define a discrete random variable.
Define a continuous random variable.
Explain what is mean[t] by the probability distribution for a random variable.
Explain what is meant by the law of larger numbers.
Calculate the mean and variable of a discrete random variable.
Calculate the mean and variance of distributions formed by combining two random variables.
8. Binomial and geometric distributions
Explain what is meant by binomial setting and binomial distribution.
Use technology to solve probability questions in a binomial setting.
Calculate the mean and variance of 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 variance.
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9. Sampling distributions
Define a sampling distribution.
Contrast bias and variability.
Describe the sampling distribution of a sample proportion (shape, center and spread).
Use a Normal approximation to solve probability problems involving the sampling distribution of a
sample proportion.
Describe the sampling distribution of the sample mean.
State the central limit theorem.
Solve probability problems involving the sampling distribution of a sample mean.
STATISTICAL INFERENCE
10. 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
to a population proportion.
Explain what is meant by the standard error, and determine the standard error of and the
standard error of.
11. Testing a claim
Explain the logic of significance testing.
List and explain the differences 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.
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Define and discuss the power of a test.
12. Significance tests in practice
Conduct one-sample and paired data t-significance tests.
Explain the differences 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.
13. Comparing two population parameters
Identify the conditions that need to be satisfied in order to do inference to comparing two
population means.
Construct a confidence interval for the difference between two population means.
Perform a significance interval 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.
Perform a significance test for the difference between two population proportions.
14. Inference for distribution of categorical variables: Chi-square procedures
Explain what is meant by a chi-square goodness of fit test.
Conduct a chi-square goodness fit test.
Given a two-way table, computer 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.
15. 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.
Conduct a test of the hypothesis that the slope of the regression line is 0 (or that the correlation is
0) in the population.