# Introduction to 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”

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

#### Type I and Type II Errors

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 9: Hypothesis Testing: Single Mean and Single Proportion"

Instructions: Please read the entire webpage in its entirety.

• Lecture: Khan Academy’s Statistics

Instructions: Please watch the brief video lecture (3:24 minutes). This lecture will discuss Type 1 Errors.

#### Distribution for Hypothesis Testing and More

Video Lecture 9: Hypothesis Testing with a Single Mean
• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 9: Hypothesis Testing: Single Mean and Single Proportion”

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”

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

Instructions: Please view the entire video lecture (14:30 minutes). This lecture will discuss large sample proportion hypothesis testing.

• Lecture: Khan Academy’s Statistics

Instructions: Please view the entire lecture (approximately 12 minutes). This lecture will discuss the difference of sample means distribution

• Lecture: Khan Academy’s Statistics

Instructions: Please watch the entire lecture (approximately 16 minutes). This lecture will discuss confidence interval of difference of means.

### 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”

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

#### 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”

Instructions: Please read the entire webpage in its entirety.

#### Comparing Two Independent Population Proportions

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions"

Instructions: Please read the entire webpage in its entirety.

• Lecture: Khan Academy’s Statistics

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.

#### Matched or Paired Samples

Video Lecture 10: Hypothesis Testing with Two Means
• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions

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"

• Assignment: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 10: Hypothesis Testing: Two Means, Paired Data, Two Proportions”

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

Instructions: Please view the entire 10-minute video lecture, which will discuss hypothesis test for difference of means.

### 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”

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

• Lecture: Khan Academy’s Statistics

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.

#### Goodness-of-Fit Test

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 11: The Chi-Square Distribution"

Instructions: Please read the entire webpage in its entirety.

#### Test of Independence

• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 11: The Chi-Square Distribution"

Instructions: Please read the entire webpage in its entirety.

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

Video Lecture 11: The Chi-Square Distribution
• Readings: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Chapter 11: The Chi-Square Distribution"

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”

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.