# Introduction to Statistical Analysis/Unit 4 Content

## Contents

## Unit 4[edit]

This content is adapted from the **Introduction to Statistics** MA121/ECON104 Course at Saylor.org.

### Subunit 4.1: The Central Limit Theorem[edit]

#### The Central Limit Theorem for Sample Means (Averages)[edit]

**Readings**: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 7: The Central Limit Theorem”

*Instructions*: Please read each of the linked sections above in their entirety.

**Lecture**: Khan Academy’s Statistics

*Instructions*: Please view the lecture in its entirety (approximately 10 minutes). This lecture will provide and introduction to the central limit theorem and the sampling distribution of the mean.

**Lecture**: Khan Academy’s Statistics

*Instructions*: Please view the both lectures, which discuss the sampling distribution of the sample mean, in their entirety (approximately 11 minutes and 13 minutes, respectively).

**Lecture**: Khan Academy’s Statistics

*Instructions*: Please view both lectures in their entirety (approximately 30 minutes total). These lectures will discuss the standard error of the mean, i.e. the standard deviation of the sampling distribution of the sample mean, and work out an example.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

#### The Central Limit Theorem for Sums[edit]

**Readings**: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 7: The Central Limit Theorem"

*Instructions*: Please read the entire webpage in its entirety.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

#### Using the Central Limit Theorem[edit]

**Readings**: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 7: The Central Limit Theorem"

*Instructions*: Please read the entire webpage in its entirety.

**Lecture**: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video lecture 7: The Central Limit Theorem”

*Instructions*: Please view the lecture to the right in its entirety.

**Assignment**: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 7: The Central Limit Theorem”

*Instructions*: Click on the hyperlink titled “**Practice: The Central Limit Theorem**”. Please solve all the problems in this section. Next, click on the hyperlink titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 13, 15, 17, 19-25. The solutions are provided below the problem. Please solve all of the problems before checking the solutions.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

### Subunit 4.2: Confidence Intervals[edit]

#### Confidence Interval, Single Population Mean, Population Standard Deviation Known, Normal[edit]

**Readings**: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 8: Confidence Intervals”

*Instructions*: Please read each of the linked sections above in their entirety.

**Lecture**: Khan Academy’s Statistics

*Instructions*: Please view the lecture in its entirety (approximately 14 minutes). In this lecture, you will learn to estimate the probability that the true population mean lies within a given range around a sample mean.

**Lecture**: Khan Academy’s Statistics

*Instructions*: Please view both lectures in their entirety (approximately 25 minutes total). In these lectures, you will learn to find the 95% confidence interval for a problem.

**Lecture**: Khan Academy’s Statistics

*Instructions*: Please view the lecture linked above (approximately 19 minutes). In this lecture, you will work out a confidence interval example

Terms of Use: Please respect the copyright and terms of use displayed on the webpage displayed above.

#### Confidence Interval, Single Population Mean, Standard Deviation Unknown, Student-T[edit]

**Readings**: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 8: Confidence Intervals"

*Instructions*: Please read the entire webpage in its entirety.

**Lecture**: Khan Academy’s Statistics

*Instructions*: Please view both lectures in their entirety (approximately 21 minutes total). These lectures will discuss constructing small size confidence intervals using t-distributions.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages displayed above.

#### Confidence Interval for a Population Proportion[edit]

**Readings**: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 8: Confidence Intervals"

*Instructions*: Please read the entire webpage in its entirety.

**Lecture**: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video lecture 8: Confidence Intervals”

*Instructions*: Please view the lecture to the right in its entirety.

**Assignment**: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 8: Confidence Intervals”

*Instructions*: Click on the hyperlink titled “**Practice 1: Confidence Intervals for Averages, Known Population Standard Deviation**” and solve problems 1-13. Next, click on the hyperlinks titled “**Practice 2: Confidence Intervals for Averages, Unknown Population Standard Deviation**” to solve problems 1-11 and “**Practice 3: Confidence Intervals for Proportions**” to solve problems 1-13. Finally, click on the hyperlink titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21. The solutions are provided below the problem. Please solve all of the problems before checking the solutions.

Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

## 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.