# Statistical Analysis/Unit 5 Content
## Unit 5

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

### Subunit 5.1: Hypothesis Testing: Single Mean and Single Proportion
#### Null and Alternate Hypotheses

* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 9: Hypothesis Testing: Single Mean and Single Proportion”
   * “Section 1: Hypothesis Testing: Single Mean and Single Proportion”
   * “Section 2: Null and Alternate Hypotheses”
Instructions: Please read each of the linked sections above in their entirety.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

#### Type I and Type II Errors

* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 9: Hypothesis Testing: Single Mean and Single Proportion"
   * "Section 3: Outcomes and the Type I and Type II Errors”
Instructions: Please read the entire webpage in its entirety.
* Lecture: Khan Academy’s Statistics
   * “Type 1 Errors”
Instructions: Please watch the brief video lecture (3:24 minutes). This lecture will discuss Type 1 Errors.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage displayed above.

#### Distribution for Hypothesis Testing and More

* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 9: Hypothesis Testing: Single Mean and Single Proportion”
   * “Section 4: Distribution Needed for Hypothesis Testing”
   * “Section 5: Assumption”
   * “Section 6: Rare Events”
   * “Section 7: Using the Sample to Support One of the Hypotheses”
   * “Section 8: Decision and Conclusion”
   * “Section 9: Additional Information”
Instructions: Please read each of the linked sections above in their entirety.
* Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 9: Hypothesis Testing with a Single Mean”
Instructions: Please view the lecture to the right in its entirety.
* Assignment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 9: Hypothesis Testing: Single Mean and Single Proportion”
   * “Practice 1: Single Mean, Known Population Standard Deviation”
   * “Practice 2: Single Mean, Unknown Population Standard Deviation”
   * “Practice 3: Single Proportion”
Instructions: Click on the hyperlinks titled “Practice 1: Single Mean, Known Population Standard Deviation,” “Practice 2: Single Mean, Unknown Population Standard Deviation,” and “Practice 3: Single Proportion” and solve the problems. Next, click on the hyperlink titled “Homework” and solve problems 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27. Please click on “[ Show Solution ]” link below the problem to check your solution.
* Lecture: Khan Academy’s Statistics
   * “Large Sample Proportion Hypothesis Testing”
Instructions: Please view the entire video lecture (14:30 minutes). This lecture will discuss large sample proportion hypothesis testing.
* Lecture: Khan Academy’s Statistics
   * “Difference of Sample Means Distribution”
Instructions: Please view the entire lecture (approximately 12 minutes). This lecture will discuss the difference of sample means distribution
* Lecture: Khan Academy’s Statistics
   * “Confidence Interval of Difference of Means”
Instructions: Please watch the entire lecture (approximately 16 minutes). This lecture will discuss confidence interval of difference of means.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage displayed above.

### Subunit 5.2: Hypothesis Testing: Two Means, Paired Data, Two Proportions
#### Comparing Two Independent Population Means with Unknown Population Standard Deviations

* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions”
   * “Section 1: Hypothesis Testing: Two Population Means and Two Population Proportions”
   * “Section 2: Comparing Two Independent Population Means with Unknown Population Standard Deviations”
Instructions: Please read each of the linked sections above in their entirety.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

#### Comparing Two Independent Population Means with Known Population Standard Deviations

* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions”
   * “Section 3: Comparing Two Independent Population Means with Known Population Standard Deviations”
Instructions: Please read the entire webpage in its entirety.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

#### Comparing Two Independent Population Proportions

* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions"
   * "Section 4: Comparing Two Independent Population Proportions”
Instructions: Please read the entire webpage in its entirety.
* Lecture: Khan Academy’s Statistics
   * “Comparing Population Proportions 1”
   * “Comparing Population Proportions 2”
   * “Hypothesis Test Comparing Population Proportions”
Instructions: Please view these three video lectures in their entirety (approximately 27 minutes total). These lectures will discuss comparing population proportions and hypothesis test comparing population proportions.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages displayed above.

#### Matched or Paired Samples

* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions
   * "Section 5: Matched or Paired Samples”
Instructions: Please read the entire webpage in its entirety.
* Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 10: Hypothesis Testing with Two Means"
Instructions: Please view the linked lecture.
* Assignment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions”
   * “Practice 1: Hypothesis Testing for Two Proportions”
   * “Practice 2: Hypothesis Testing for Two Averages”
Instructions: Click on the hyperlinks titled “Practice 1: Hypothesis Testing for Two Proportions” and “Practice 2: Hypothesis Testing for Two Averages” and solve the problems. Next, click on the hyperlink titled “Homework” and solve problems 1, 5, 7, 9, 11, 15, 17, 21, 23, 27, 29, 33, 35, 43-48. Please click on “[ Show Solution ]” link below the problem to check your solution.
* Lecture: Khan Academy’s Statistics
   * “Hypothesis Test for Difference of Means”
Instructions: Please view the entire 10-minute video lecture, which will discuss hypothesis test for difference of means.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage displayed above.

### Subunit 5.3: Chi-Square Distribution

5.3.1 Notation and Facts
* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 11: The Chi-Square Distribution”
   * “Section 1: The Chi-Square Distribution”
   * “Section 2: Notation”
   * “Section 3: Facts About the Chi-Square Distribution”
Instructions: Please read each of the linked sections above in their entirety.
* Lecture: Khan Academy’s Statistics
   * “Chi-Square Distribution Introduction”
   * “Pearson's Chi Square Test (Goodness of Fit)”
   * “Contingency Table Chi-Square Test”
Instructions: Please view all three video lectures in their entirety (approximately 40 minutes total). These lectures will provide an introduction to the Chi-Square distribution as well as the Chi-Square test.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages displayed above.

#### Goodness-of-Fit Test

* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 11: The Chi-Square Distribution"
   * "Section 4: Goodness-of-Fit Test”
Instructions: Please read the entire webpage in its entirety.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

#### Test of Independence

* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 11: The Chi-Square Distribution"
   * "Section 5: Test of Independence”
Instructions: Please read the entire webpage in its entirety.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages.

#### Test of a Single Variance (Optional)

* Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 11: The Chi-Square Distribution"
   * "Section 6: Test of a Single Variance (Optional)”
Instructions: Please read the entire webpage in its entirety.
* Lecture: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Video Lecture 11: The Chi-Square Distribution”
Instructions: Please view the lecture to the right in its entirety.
* Assignment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 11: The Chi-Square Distribution”
   * “Practice 1: Goodness-of-Fit Test”
   * “Practice 2: Contingency Tables”
   * “Practice 3: Test of a Single Variance”
Instructions: Click on the hyperlinks titled “Practice 1: Goodness-of-Fit Test,” “Practice 2: Contingency Tables,” and “Practice 3: Test of a Single Variance” and solve the problems. Next, click on the hyperlink titled “Homework” and solve odd numbered problems between 3-37. 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

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.
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