The following material is from section 9.1 in the textbook.

Introduction

A hypothesis test is a way of determining if a hypothesis about a population value, like the mean, is true. For example, if I think that the average GPA of students at Moraine is higher than 2.8, then I could use a hypothesis test and a sample to determine if this is true. Hypothesis testing like this is used throughout business, science, and industry.

Lecture video - the idea of hypothesis tests

In this video, you will see what the basic concept of a hypothesis test is and how to set up the null and alternative hypotheses for a given test.

The p-value method

As mentioned in the overview, there are two approaches to hypothesis tests: the p-value method and the rejection region method. The p-value method uses the following technique:

Calculate the p-value using technology. The p-value is the probability of a sample like ours or more extreme, assuming the null hypothesis is true.
Compare the p-value to the significance level alpha ().
- If p-value $\le\alpha$ , reject H0.
- If p-value > $\alpha$ , fail to reject H0.

t-test vs z-test

When testing the mean, you will either use a z-test or a t-test. The rule is the same as for confidence intervals: if $\sigma$ is known, use a z-test. Otherwise, use a t-test.

Lecture video - z-test and t-tests using the p-value method

The following video will walk you through applying the p-value method to these types of problems.

Click NEXT to study the rejection region method for z-tests and t-tests.