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Confidence intervals and sample sizes estimations

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Learn confidence intervals and determining sample sizes in statistics

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- 2 hours on-demand video
- 5 Supplemental Resources
- Full lifetime access
- Access on mobile and TV

- Certificate of Completion

What Will I Learn?

- By the end of the course, you will understand the concepts of confidence intervals and determining sample sizes
- By the end of the course, you will understand how to interpret confidence intervals
- By the end of the course, you will be able to calculate confidence intervals about the population mean
- By the end of the course, you will be able to calculate confidence intervals about the population proportion
- By the end of the course, you will be able to calculate confidence intervals about the population variance
- By the end of the course, you will be able to calculate confidence intervals about the population standard deviation
- By the end of the course, you will be able to calculate sample sizes when estimating a population mean or proportion

Requirements

- Understanding of the Normal distribution is Required
- Please the course entitled: "Learn the Normal or Gaussian distribution"

Description

Calculating confidence intervals and determining sample sizes is an important topic of statistical inference. This is one of the most practical areas of statistics that allows the student to learn the concepts and apply them to real world situations.

This course explains the concepts in an easy to understand way. This is reinforced with fully solved and explained problems to highlight all the important details the student needs to pay attention to. In addition, the student will have the opportunity to take selected quizzes that serve as check points to determine if each concept is well understood.

The course includes tables of the standard normal distribution, the Student t distribution and the Chi square distribution. In addition, you will be given the opportunity to take a final test to check your understanding of the overall material.

It may take between two weeks to a month to finish this material depending on how much time is devoted to the course as well as the student prior preparation. It is important to realize that this course prerequisite is the knowledge of the Normal distribution. The student can achieve that requirement by taking my course "Learn the Normal or Gaussian distribution" first.

This topic of confidence intervals and determining sample sizes is a required section for students learning statistics. The material is also very useful to professionals in many fields who want to apply statistical concepts in their daily work.

Who is the target audience?

- College students taking an introductory statistics course
- Business professionals interested in statistical applications
- Anyone interested in understanding confidence intervals and calculating sample sizes

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Curriculum For This Course

Expand All 30 Lectures
Collapse All 30 Lectures
02:08:46

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What we will learn
1 Lecture
08:03

Information about the course: Confidence intervals and Determining Sample Sizes

Preview
08:03

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Course documents
5 Lectures
00:00

Table of the standard normal table with the negative Z values

Standard normal tables

1 page

This table shows the Z the values corresponding to a given area to the left of those values.

Percentiles of the standard normal table

1 page

Table of Student t distribution

1 page

Table of the chi square distribution part 1.

Tables of the chi square distribution

5 pages

This test covers essential sections of the course and is designed to check for mastery of the course content.

Final test on confidence intervals and sample sizes estimation

5 pages

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Confidence interval concepts
3 Lectures
13:06

This lectures covers basic concepts related to point estimations and their desired properties

Preview
03:42

This lecture talks about the basic concepts of confidence intervals or interval estimates and explains confidence levels. It also provides a thorough explanation of what the confidence levels mean and how to interpret them.

Definitions and interpretations of confidence intervals

03:37

This flowchart helps to determine when we can use the normal distribution or the Student t distribution for constructing the confidence intervals for the population means.

Flowchart to help determine when to use Student t or Normal distribution

05:47

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Confidence interval for the population mean using the Normal distribution
4 Lectures
19:12

In this video, we talk about the effect of sample size and confidence level on the width of the confidence interval. We also talk about the effect of increasing or decreasing the margin of error on the confidence interval.

Observations about confidence intervals

04:44

In this lecture we cover the confidence interval for the population mean when the sample size is large or when the sample size is small and the population standard deviation is known. In those two cases, we use the normal distribution in the calculation of the confidence interval critical values.

Confidence interval for the population mean when the sample size is large

03:20

In this lecture, we show how to obtain the critical values (Z sub alpha over 2) that are used for computing the confidence intervals.

Finding the critical values which are read: Z sub alpha divided by two

04:22

In this video, we show examples about computing the confidence interval for the population mean when the sample size selected is large. In this case, we use the critical value based on the normal distribution.

We also show a special case where we are computing the confidence interval for the population mean when the sample size is small but the we are sampling from a population that is normally distributed with mean U and known standard deviation sigma. In that case also, we use the critical value based on the normal distribution.

Examples calculating confidence intervals using the Normal distribution

06:46

In this quiz, you will compute a confidence interval for the population when the selected sample size is large

Computing a confidence for the mean, when sample size is large

2 questions

In this quiz, we you are asked to calculate a confidence interval of the population mean.

Confidence interval for the population mean

1 question

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Confidence interval about the population mean using the Student t distribution
3 Lectures
17:31

In this lecture, we talk about the confidence interval for the population mean when the sample size is small (n < 30), the population standard is small and we are sampling from a population that is normally or approximately normally distributed. We talk about the Student t distribution and shows how it looks like compare to the normal distribution.

Confidence interval for the pop. mean when the sample size is small: Student t

05:45

In this lecture, we show how the confidence interval for the population mean when the sample size is small and the population standard deviation sigma is unknown is calculated.

Confidence interval for the population mean when the sample size is small

04:13

In this lecture, we illustrate how to compute confidence intervals using the Student t distribution. Practical examples are given to reinforce the understanding of the Student t distribution.

Practical examples calculaiting confidence intervals using the Student t

07:33

The purpose of this quiz is calculate a confidence interval for the population mean when the sample size is small, the population standard deviation is unknown and the population is assumed to be approximately normally distributed.

Confidence interval for the mean when sample size is small

1 question

In this quiz, you will compute a confidence interval for the population mean when the sample size is small.

Confidence interval for the pop mean when sample size is small

1 question

In this quiz, you are asked to calculate a confidence interval about the population mean.

Confidence interval about the pop mean using Student t (Part 3)

1 question

Quiz about using the student t distribution to ompute confidence intervals

Student t (Part 2)

1 question

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Confidence Interval about a population proportion or percent p
3 Lectures
13:30

In this lecture, we talk about how to estimate a population proportion p with the sample proportion. We discuss the conditions that must be met for construction a confidence interval about the population proportion

Inference about a population proportion p.

03:03

In this lecture we discuss the formula for the confidence interval for the population proportion or percent p.

Confidence Interval about a population proportion or percent p

02:42

In this lecture, we show practical examples for computing the confidence interval of the population proportion or percent.

Practical examples calculaiting confidence intervals for the pop. proportion

07:45

In this quiz, you are asked to compute a confidence interval of the population proportion

Confidence interval about a population proportion

1 question

In this quiz, you are asked to compute a confidence interval of a population proportion

Confidence interval about a population proportion (Part 2)

1 question

In this quiz, you are asked to compute a confidence interval of the population proportion

Confidence interval about a population proportion (Part 3)

1 question

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Determining sample sizes when estimating a population mean
2 Lectures
10:51

In this lecture, we talk about the formula for determining the sample size when the purpose of the study is to estimate a population mean.

Determining sample sizes when estimating a population mean

03:25

In this video, we show practical examples about how to find sample sizes when the purpose is to estimate a population mean.

Practical exercises about determining sample sizes when we are estimating a mean

07:26

In this quiz, we will calculate the sample size needed when the purpose of the study is to estimate a population mean.

Determining a sample size needed when estimating a population mean

1 question

In this quiz, you will compute the sample size needed when the purpose of the study is to estimate a population mean.

Sample size needed to estimate a population mean

1 question

In this quiz, you will calculate the sample size needed to estimate a population mean

Determining sample size when estimating a population mean (part 2)

1 question

In this quiz, you are asked to calculate the sample size needed when estimating a population mean

Determining sample size when estimating a population mean (part 3 )

1 question

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Determining sample sizes when estimating a population proportion
2 Lectures
09:30

In this lecture, we discuss the formula for determining sample sizes when we want to estimate a population proportion.

Determining sample sizes when estimating a population proportion

04:30

In this lecture, we show practical examples about determining sample sizes when we are estimating a population proportion.

Practical exercises about finding sample sizes when estimating a proportion

05:00

The purpose of this quiz is to determine the sample size needed to estimate a population proportion.

Sample size needed to estimate a population proportion

1 question

In this quiz, we need to calculate the sample size needed to estimate a population proportion

Determining sample size when estimating a population proportion (part 3)

1 question

In this quiz, you will calculate the required sample size needed when we are estimating a population proportion

Sample size needed to estimate a population proportion (2)

1 question

In this quiz, you are asked to determine the sample size needed when we are estimating a population proportion.

Determining sample size when estimating a population proportion (part 2)

1 question

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Confidence interval for the population variance and standard deviation
6 Lectures
17:38

In this lecture, we talk about the chi square distribution. In the end, we cover the point estimates about the population variance and standard deviation.

Understanding the chi square distribution

02:44

In this lecture, we discuss the properties of the chi-square distribution.

Properties of the Chi square distribution

01:25

In this lecture, we show to read the critical values of the chi square distribution for the confidence interval of the population variance and standard deviation. These tables values (critical values) are essential in the calculation of the confidence interval for the population mean and standard deviation.

Reading the critical or table values in the chi square distribution table

05:05

In this lecture, we talk about the formulas for calculating the confidence interval for a population variance and standard deviation using the chi square distribution.

Confidence interval about the population variance and standard deviation

01:35

In this lecture,we use a real world problem to show how to compute a confidence interval about the population variance.

Practical example: confidence interval about the population variance

03:03

In this lecture, we are using a real world example to illustrate how we compute the confidence interval for the population standard deviation.

Practical example: confidence interval for the population standard deviation

03:46

In this quiz, you will calculate the confidence interval of a population variance

Confidence interval for a population variance

1 question

In this quiz, you will calculate a confidence interval of a population standard deviation

Confidence interval for a population standard deviation

1 question

In this quiz, you are asked to compute a confidence interval of the population standard deviation

Confidence interval for a population standard deviation (Part 2)

1 question

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Conclusion and final remarks
1 Lecture
06:25

Concluding remarks and what is next

06:25

About the Instructor

Adjunct faculty of Math and Statistics

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