This chapter uses the example of whether an auto mechanic’s salary relates to his years of experience to introduce linear regression and correlation. It covers the basic ideas of linear regression and correlation, creating and interpreting a line of best fit, calculating and interpreting the correlation coefficient, and identifying outliers.
Do two variables move together?
The chapter opens with the question of whether two numeric variables are related, using the pairing of exam grades on two tests and of an auto mechanic’s pay against years of experience as running examples, and discusses the basic ideas of linear regression and correlation as tools for answering it.
The line of best fit and the correlation coefficient
Students learn to create and interpret a line of best fit through a scatter of paired data points, and to calculate and interpret the correlation coefficient, a single number summarizing how strong and in what direction the linear relationship between the two variables runs.
Identifying outliers
The chapter also covers calculating and interpreting outliers, points that fall unusually far from the line of best fit, teaching students to recognize when a data point may be distorting the regression results and should be examined rather than automatically included in the analysis.
This chapter uses the example of comparing breakfast habits east and west of the Mississippi River to introduce hypothesis testing across two groups. It covers classifying hypothesis tests by type, testing two population means with both known and unknown standard deviations, testing two population proportions, and handling matched or paired samples.
Classifying two-sample hypothesis tests
The chapter opens by teaching students to classify hypothesis tests by type, since comparing two groups requires first identifying whether the groups are independent or matched, and whether the comparison concerns means or proportions, before the correct testing procedure can be chosen.
Testing two population means
Students learn to conduct and interpret hypothesis tests for two population means both when the population standard deviations are known and when they are unknown, mirroring the one-sample case from the previous chapter but now comparing two groups directly, such as breakfast habits in different regions.
Testing proportions and matched pairs
The chapter also covers conducting and interpreting hypothesis tests for two population proportions and for matched or paired samples, where the same subjects are measured under two different conditions, requiring a method that accounts for the dependence between the paired observations rather than treating them as two independent groups.
This chapter uses the example of testing a dog breeder’s claim about the number of spots on a Dalmatian to teach hypothesis testing with a single sample. It covers differentiating Type I and Type II errors, describing hypothesis testing in general and in practice, and conducting tests for a population mean and a population proportion.
Making a decision about a claim
The chapter frames hypothesis testing as a way to make a decision about a parameter rather than simply estimate it, illustrated with a car dealer’s advertised claim or a dog breeder’s claim about spot counts, teaching students to describe hypothesis testing in general and in practice as a structured way of evaluating such claims against sample evidence.
Type I and Type II errors
Students learn to differentiate between a Type I error, incorrectly rejecting a true claim, and a Type II error, failing to reject a false claim, a distinction the chapter treats as central to understanding what a hypothesis test’s conclusion does and does not guarantee.
Testing means and proportions
The chapter covers conducting and interpreting hypothesis tests for a single population mean, both when the population standard deviation is known and when it is unknown, as well as for a single population proportion, giving students the complete one-sample toolkit before extending it to two samples in the next chapter.
This chapter introduces the F distribution and one-way ANOVA as tools for statistical applications spanning psychology, social science, and the natural sciences. It covers interpreting the F distribution as group number and sample size change, its two uses in one-way ANOVA and testing two variances, and conducting and interpreting both types of test.
Interpreting the F distribution
The chapter teaches students to interpret the F probability distribution as the number of groups being compared and the sample size change, establishing the distribution’s shape as something that shifts with the structure of the data rather than remaining fixed, before applying it to specific hypothesis tests.
Two uses: ANOVA and testing two variances
Students learn to discuss the F distribution’s two main uses: one-way ANOVA, which compares averages across several groups at once, and the test of two variances, which compares the spread of two groups directly, framing the F distribution as the shared statistical tool behind both kinds of question.
Conducting and interpreting the tests
Beyond recognizing when each test applies, the chapter has students conduct and interpret one-way ANOVA and conduct and interpret hypothesis tests of two variances, working through the full process from stating hypotheses to reaching a conclusion about whether the observed differences are statistically meaningful.
This chapter uses the example of lightning striking the ground during a thunderstorm to introduce discrete random variables and probability distribution functions. It covers calculating and interpreting expected values, and studies the binomial, Poisson, geometric, and hypergeometric probability distributions, along with how to classify word problems by which distribution applies.
Probability distribution functions
The chapter opens by asking students to recognize and understand discrete probability distribution functions in general, building the foundation for calculating and interpreting expected values, the long-run average outcome of a random variable, before moving into specific named distributions.
Four named discrete distributions
Students learn to recognize and apply four specific discrete distributions: the binomial probability distribution, the Poisson probability distribution, the geometric probability distribution, and the hypergeometric probability distribution, each suited to a different kind of counting problem, from the number of successes in a fixed number of trials to the number of events in a fixed interval.
Classifying word problems by distribution
Because real problems are described in words rather than handed over as ready-made formulas, the chapter emphasizes classifying discrete word problems by which distribution they call for, a skill illustrated with the lightning example, where students must recognize the setup as matching a specific distribution before any calculation begins.
