# Introduction to Statistical Analysis/Unit 5 Navigation

This is the main navigation page for Unit 5 of the course **Introduction to Statistical Analysis**, developed using openly licensed materials from Saylor.org's **Introduction to Statistics**. Below you will find a full description of Unit 5 in general, as well as for each subunit. Follow the links within each subunit description to access particular topics, or proceed directly to the Unit 5 Content Page.

**UNIT 5: HYPOTHESIS TESTING**[edit]

One of the major goals in statistics is to use the information you collect from a sample to get a better idea of the entire population you’re interested in. In this unit, you will learn about hypothesis testing, which enables us to achieve that goal.

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 also teach you how to conduct hypothesis tests and 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. You will have to make decisions about 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. Then, you will learn to compare sample characteristics to assumptions to see whether there is enough data to accept or reject the null hypothesis. 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. The unit will finally conclude with an introduction to Chi-distributions and their applications.

### Time Advisory[edit]

Time Advisory: This unit will take you 15 hours to complete.

- Subunit 5.1: 5 hours
- Subunit 5.2: 5 hours
- Subunit 5.3: 5 hours

### Learning Outcomes[edit]

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

- Differentiate between Type I and Type II Errors.
- Describe hypothesis testing in general and in practice.
- Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.
- Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.
- Conduct and interpret hypothesis tests for a single population proportion.
- Classify hypothesis tests by type.
- Conduct and interpret hypothesis tests for two population means, population standard deviations known.
- Conduct and interpret hypothesis tests for two population means, population standard deviations unknown.
- Conduct and interpret hypothesis tests for two population proportions.
- Conduct and interpret hypothesis tests for matched or paired samples.
- Interpret the chi-square probability distribution as the sample size changes.
- Conduct and interpret chi-square goodness-of-fit hypothesis tests.
- Conduct and interpret chi-square test of independence hypothesis tests.
- Conduct and interpret chi-square single variance hypothesis tests.

### Subunits[edit]

Unit five consists of three main topics:

#### Hypothesis Testing: Single Mean and Single Proportion[edit]

- 5.1.1: Null and Alternate Hypotheses
- 5.1.2: Type I and Type II Errors
- 5.1.3: Distribution for Hypothesis Testing and More

#### Hypothesis Testing: Two Means, Paired Data, Two Proportions[edit]

- 5.2.1: Comparing Two Independent Population Means with Unknown Population Standard Deviations
- 5.2.2: Comparing Two Independent Population Means with Known Population Standard Deviations
- 5.2.3: Comparing Two Independent Population Proportions
- 5.2.4: Matched or Paired Samples

#### Chi-Square Distribution[edit]

- 5.3.1: Notation and Facts
- 5.3.2: Goodness-of-Fit Test
- 5.3.3: Test of Independence
- 5.3.4: Test of a Single Variance (Optional)

## About the Resources in This Course[edit]

This course project draws upon three main types of resources:

The first are readings and video lectures from Barbara Illowsky and Susan Dean’s Collaborative Statistics, which is available freely under a Creative Commons Attribution 2.0 Generic (CC BY 2.0) license from the following location: http://cnx.org/content/col10522/latest/

The second type of resources in this course are lectures from Kahn Academy. These lectures are available under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0) license. Kahn Academy has many lectures available from http://www.khanacademy.org/

Finally, the above resources have been woven together and organized into a format analogous to a traditional college-level course by professional consultants that work as experts within the subject area. This process was facilitated by The Saylor Foundation. Additionally, if you have worked through all of the material contained in this project, you may be interested in taking the final exam provided by Saylor.org or completing other courses available there that are not yet on Wikiversity.