### Unit 5: Hypothesis Test

A hypothesis test involves collecting and evaluating data from a sample. The data gathered and evaluated is then used to make a decision as to whether or not the data supports the claim that is made about the population. This unit will teach you how to conduct hypothesis tests and how to identify and differentiate between the errors associated with them.

Many times, you need answers to questions in order to make efficient decisions. For example, a restaurant owner might claim that his restaurant's food costs 30% less than other restaurants in the area, or a phone company might claim that its phones last at least one year more than phones from other companies. In order to decide whether it would be more affordable to eat at the restaurant that "costs 30% less" or another restaurant in the area, or in order to decide which phone company to choose based on the durability of the phone, you will have to collect data to justify these claims. The process of hypothesis testing is a way of decision-making. In this unit, you will learn to establish your assumptions through null and alternative hypotheses. The null hypothesis is the hypothesis that is assumed to be true and the hypothesis you hope to nullify, while the alternative hypothesis is the research hypothesis that you claim to be true. This means that you need to conduct the correct tests to be able to accept or reject the null hypothesis. You will learn how to compare sample characteristics to see whether there is enough data to accept or reject the null hypothesis.

**Completing this unit should take you approximately 4 hours.**

Upon successful completion of this unit, you will be able to:

- differentiate between type I and type II errors, and find the probability of these errors;
- describe and conduct hypothesis testing, calculate the p-value, and accept or reject the null hypothesis; and
- explain how to conduct hypothesis tests for a single population mean and population proportion, when the population standard deviation is unknown; perform this task; and interpret the results.

### 5.1: Elements of Hypothesis Testing

### 5.1.1: Setting up Hypotheses

- This section discusses the logic behind hypothesis testing using concrete examples and explains how to set up null and alternative hypothesis. It explains what Type I and II errors are and how they can occur. Finally, it introduces one-tailed and two-tailed tests and explains which one you should use for testing purposes.

### 5.1.2: Interpreting Hypotheses Testing Results

- This section explains what the observed significance of a test is, including how to compute and use it in the p-value approach.
First, this section discusses whether rejection of the null hypothesis should be an all-or-none proposition. Then, it discusses how to interpret non-significant results; for example, it explains why the null hypothesis should not be accepted or should be accepted with caution. It also describes how a non-significant result can increase confidence that the null hypothesis is false.

- Read this section on the two types of errors in hypothesis testing and some examples of each.
Watch these videos on hypothesis testing.

### 5.1.3: Steps in Hypothesis Testing and Its Relation to Confidence Intervals

- This section lists four key steps in hypothesis testing and explains the close relationship between confidence intervals and significance tests.

### 5.2: Tests of Population Means

### 5.2.1: Testing Single Mean

This section shows how to test the null hypothesis that the population mean is equal to some hypothesized value, using a very concrete example. In this example, all the main elements of hypothesis testing come in to play a role.

This section talks about using the central limit theorem to test a population mean when the sample size is large. It also addresses how to interpret the test results in the application background. Then, it discusses testing a population mean when the sample size is small, outlines a five-step testing procedure, and illustrates the procedure with an example. Study the example carefully and complete the relevant exercises and applications. Finally, it talks about large sample tests for a population proportion. The critical value and p-value approach are introduced based on a standardized test statistic.

### 5.2.2: Testing the Difference between Two Means

This section covers how to test for differences between means from two separate groups of subjects and gives an example of opinions on animal research. The detailed testing procedure is carried out using the standard steps in hypothesis testing.

Watch these videos on the difference of means.

### 5.3: Chi-Square Distribution

- Read this section, which discusses contingency tables, and answer the questions at the end of the section. While this section is optional, studying it may help you if you wish to take the Saylor Direct Credit exam for this course.
- Read these sections, which discuss chi-square distributions and how to test the goodness of fit. While these sections are optional, studying them may help you if you wish to take the Saylor Direct Credit exam for this course.
- Watch these videos, which discuss chi-square distributions, goodness of fit, and contingency tables.

### 5.4: Comparing the Proportions of Populations

Watch these videos, which discuss comparing population proportions. While these videos are optional, studying these topics may help you if you are interested in taking the credit-aligned exam that is linked with this course.

### Unit 5 Assessment

- Receive a grade
Take this assessment to see how well you understood this unit.

- This assessment
**does not count towards your grade**. It is just for practice! - You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.

- This assessment