http://www.ck12.org Chapter 8. Hypothesis Testing
8.1 Hypothesis Testing and the P-Value
Learning Objectives
- Develop null and alternative hypotheses to test for a given situation.
- Understand the critical regions of a graph for single- and two-tailed hypothesis tests.
- Calculate a test statistic to evaluate a hypothesis.
- Test the probability of an event using theP-value.
- Understand Type I and Type II errors.
- Calculate the power of a test.
Introduction
In this chapter we will explorehypothesis testing,which involves making educated guesses about a population
based on a sample drawn from the population. Most times, hypothesis testing involves making guesses about the
difference between the hypothesized value of the mean of an overall population and that of the sample. This is
often used in statistics to analyze the likelihood that a population has certain characteristics. For example, we can
use hypothesis testing to analyze if a senior class has a particular average SAT score or if a prescription drug has a
certain proportion of the active ingredient.
A hypothesis is simply an educated guess about a characteristic or set of facts. When performing statistical analyses,
our hypotheses provide the general framework of what we are testing and how to perform the test. These tests are
never certain and we can neverproveordisprovehypotheses with statistics, but the outcomes of these tests provide
information that either helps support or refute the hypothesis itself.
In this section we will learn about the different types of hypothesis testing, how to develop hypotheses, how to
calculate statistics to help support or refute the hypotheses and understand the errors associated with hypothesis
testing.
Developing Null and Alternative Hypotheses
As mentioned in the introduction, hypothesis testing involves testing the difference between a hypothesized value of
the mean of an overall population and the mean calculated from a sample. In hypothesis testing, we are essentially
determining the magnitude of the difference between the mean of the sample and they hypothesized mean of the
population. If the difference is very large, we reject our hypothesis about the population. If the difference is very
small, we do not. Below is an overview of this process.