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What the exam asks for

• Identify samples, populations, variables, and study questions, then keep conclusions within the scope of the data collection.
• Choose and interpret categorical tables and graphs, and quantitative displays such as histograms, dotplots, and boxplots.
• Describe and compare quantitative distributions by shape, center, spread, and unusual features; select suitable summary statistics.
• Distinguish sampling procedures and sources of bias from experimental design features such as random assignment, control, and confounding.

Common slips to watch for

• Treating a sample statistic as if it describes the whole population without accounting for how the sample was selected.
• Describing a distribution without context or omitting a feature such as skew, outliers, gaps, or clusters.
• Confusing random sampling, which supports generalization, with random assignment, which supports cause-and-effect conclusions.
• Choosing the mean and standard deviation for strongly skewed data with outliers, or using a graph that obscures category proportions.

What the exam asks for

• Use two-way tables and graphical summaries to compare conditional, marginal, and joint patterns between categorical variables.
• Set up chance models, identify events, and apply complements, intersections, unions, conditional probability, and independence rules.
• Represent discrete random variables with complete probability distributions; calculate and interpret their means and standard deviations.
• Check binomial conditions and use normal models and sampling distributions to reason about probabilities, variability, and the effect of sample size.

Common slips to watch for

• Reversing the condition in a conditional probability or using a joint proportion when a conditional proportion is required.
• Assuming events are independent or mutually exclusive without checking the relevant probability relationship.
• Leaving out possible outcomes from a random-variable distribution or using probabilities that do not sum to one.
• Applying a binomial or normal model without checking its conditions, or confusing the spread of individual values with the spread of sample statistics.

What the exam asks for

• Define population proportions and differences in context, and connect sample proportions with their sampling distributions and estimator properties.
• Select one- or two-proportion intervals and tests, state hypotheses in context, and verify randomization, independence, and success-failure conditions.
• Calculate or interpret test statistics, p-values, confidence intervals, and the implications of Type I and Type II errors.
• For two-way categorical data, choose a homogeneity or independence test, find expected counts, and interpret the chi-square result in context.

Common slips to watch for

• Using the observed sample proportion rather than the null value to calculate a one-proportion test standard error.
• Writing hypotheses about sample statistics instead of population proportions, or reversing the direction of the alternative.
• Treating a p-value as the probability that the null hypothesis is true, or stating a conclusion without linking it to the context.
• Using separate rather than pooled proportions for a two-proportion test, or confusing the purposes of homogeneity and independence tests.

What the exam asks for

• Choose t procedures for means and mean differences when population standard deviations are unknown; distinguish independent samples from paired differences.
• State population mean parameters and hypotheses in context, then check randomization, independence, the 10% condition, and distributional requirements.
• Construct and interpret t intervals, including what repeated-sampling confidence means and whether an interval for a difference contains zero.
• Calculate and interpret t statistics and p-values using appropriate standard errors and degrees of freedom.

Common slips to watch for

• Using a two-sample procedure for paired observations instead of analyzing the within-pair differences.
• Using a z procedure when the population standard deviation is unknown, or selecting degrees of freedom without regard to the t procedure.
• Claiming an interval gives the probability that the fixed parameter lies in the observed interval.
• Reporting a p-value or interval conclusion without identifying the population mean or mean difference and its context.

What the exam asks for

• Construct and read scatterplots with explanatory and response variables on the correct axes; describe form, direction, strength, and unusual points.
• Interpret correlation as describing the direction and strength of a linear relationship, not every feature of a relationship.
• Use a fitted line to predict responses, distinguishing interpolation from less-reliable extrapolation.
• Calculate and interpret residuals, and use residual plots to assess whether a linear model is appropriate.
• Interpret slope, intercept, and squared correlation in context, including what variation the linear association accounts for.

Common slips to watch for

• Putting the response variable on the horizontal axis or describing a scatterplot without addressing its direction, form, and strength.
• Treating correlation as evidence of causation or as a description of nonlinear association.
• Confusing observed and predicted values when calculating residuals, or reversing the residual sign.
• Extrapolating beyond the observed x-values without noting the prediction’s reduced reliability.