### 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 12 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

Read sections 2, 4, and 5 from Chapter 11, and complete the questions at the end of each section. Section 2 discusses the logic behind hypothesis testing using concrete examples and explains how to set up null and alternative hypothesis. Section 4 explains what Type I and II errors are and how they can occur. Section 5 introduces one-tailed and two-tailed tests and explains which one should be used for the testing purpose.

### 5.1.2: Interpreting Hypotheses Testing Results

Read section 3 from Chapter 8. This section explains what the observed significance of a test is; in particular, this reading tells us how to compute it and use it in the p-value approach. Study the examples, and complete the odd-numbered exercises at the end of the section before checking the answers.

Read sections 6 and 7 from Chapter 11, and complete the questions at the end of each section. Section 6 discusses whether rejection of the null hypothesis should be an all-or-none proposition. Section 7 discusses how to interpret non-significant results; for example, it explains why the null hypothesis should not be accepted, or accepted with caution. This section also describes how a non-significant result can increase confidence that the null hypothesis is false.

Locate and read the section titled, Type I and Type II Errors, on the linked page, which discusses two types of errors in hypothesis testing, using numerous examples.

Watch these videos on hypothesis testing.

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

Read sections 8 and 9 from Chapter 11. Also, complete the questions at the end of each section. Section 8 lists four key steps in hypothesis testing. Section 9 explains the close relationship between confidence intervals and significance tests.

Watch the videos titled "Significance Level in Hypothesis Testing" and "Hypothesis Testing Example." The first video shows you how to make a decision in a hypothesis test based on the significance level of critical values. The second video provides an example of a left tailed hypothesis test.

### 5.2: Tests of Population Means

### 5.2.1: Testing Single Mean

Read section 2 from Chapter 12. 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. There are 9 questions at the end of the section to help your understanding of the material.

Read section 2, section 4, and 5. Complete the odd-numbered problems at the end of each section before checking your answers.

Section 2 talks about how to use 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. Section 4 discusses testing a population mean when the sample size is small. This section outlines a five-step testing procedure and then illustrates this procedure with an example. Study the example carefully and complete the relevant exercises and applications. Section 5 talks about large sample tests for a population proportion. Both the critical value and p-value approach are introduced based on a standardized test statistic. Once again, this section illustrates the five-step testing procedure in Examples 12-15.

### 5.2.2: Testing the Difference between Two Means

Read section 4 from Chapter 12. Also, answer the questions at the end of this section. This section covers how to test for differences between means from two separate groups of subjects. This reading presents an example of opinions on animal research, and the main interest is to test for gender difference at the population level. The detailed testing procedure is carried out by 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 credit-aligned exam that is linked with this course.

Read these two sections, which discuss chi-square distributions and how to test goodness of fit. Also, answer the questions at the end of each section. While these sections are optional, studying them may help you if you wish to take the credit-aligned exam that is linked with 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

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