# Statistical Analysis/Unit 4 Content

## Unit 4

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

### Subunit 4.1: The Central Limit Theorem

#### The Central Limit Theorem for Sample Means (Averages)

• 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.

#### The Central Limit Theorem for Sums

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

Instructions: Please read the entire webpage in its entirety.

#### Using the Central Limit Theorem

• 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.

### Subunit 4.2: Confidence Intervals

#### Confidence Interval, Single Population Mean, Population Standard Deviation Known, Normal

• 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

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

• 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.

#### Confidence Interval for a Population Proportion

• 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.