Hypothesis Testing with One Sample

Summary :

This chapter situates hypothesis testing within the scientific method, using the economic theory of consumer choice and the demand curve as an example of how a theory generates a testable prediction. It covers null and alternative hypotheses, Type I and Type II errors, and the distributions used depending on what is known about the population.

Hypothesis testing as part of the scientific method

The chapter frames statistical hypothesis testing as the formal mechanism behind the scientific method, where a theory or model built on stated assumptions leads to predictions, or hypotheses, that can be tested; it illustrates this with microeconomic consumer choice theory, whose assumptions predict the negative-sloped demand curve, a prediction statistics is used to test rather than simply assert.

Null and alternative hypotheses, Type I and Type II errors

Every hypothesis test begins by stating two competing hypotheses, the null and the alternative, and the chapter explains the two ways a test can go wrong: a Type I error, rejecting a true null hypothesis, and a Type II error, failing to reject a false one, along with how the outcomes of a test relate to these error types.

Choosing the right distribution for the test

Which distribution underlies a one-sample hypothesis test depends on what is known about the population, and the chapter covers testing a single population mean when the standard deviation is known, when it is unknown, and testing a single population proportion, connecting each case back to the sampling distributions developed earlier in the course.