About This Chapter
Inference About a Mean - Chapter Summary
Begin this chapter with a lesson showing you how the central limit theorem can be used to determine the probability of a sample mean. You can also find out how to calculate and interpret confidence intervals for expected values and estimate confidence intervals by determining the sample size. You'll learn the differences between biased and unbiased estimators as well.
Additional topics of instruction cover the uses of hypothesis testing to evaluate inferences made about data collected from observational studies or experiments. You can also study the impact of effect size on this process. Wrap up your study with lessons that illustrate the differences between type I and type II errors by describing their relationship to the null hypothesis. This chapter is designed to familiarize you with the following:
- The central limit theorem
- Confidence intervals
- Biased and unbiased estimators
- Hypothesis testing
Let our informed and experienced instructors help you explore methods used to analyze statistical data with the lessons included in this chapter. The short instructional videos feature tags you can use to navigate between the main ideas discussed by our instructors. There are also matching transcripts if you'd prefer to access content in a different format. Both materials can prepare you for the multiple-choice questions included at the end of each lesson. These might prove useful if you're looking to confirm your understanding of the lesson topics or chart your progress through the course.
1. Finding Probabilities About Means Using the Central Limit Theorem
The central limit theorem provides us with a very powerful approach for solving problems involving large amount of data. In this lesson, we'll explore how this is done as well as conditions that make this theorem valid.
2. Calculating Confidence Intervals, Levels & Coefficients
In this lesson, you're going to learn about confidence intervals, confidence levels, and coefficients, and how they relate to point estimates and interval estimates.
3. Determining the Sample Size to Estimate Confidence Intervals: Definition & Process
In this lesson, you will learn how to determine the most appropriate sample size to find the confidence interval we need using a specific case example.
4. Biased & Unbiased Estimators: Definition & Differences
When dealing with statistics, you've probably heard about why it is wise to avoid biased estimators. However, as this lesson proves, sometimes a biased estimator can be pretty useful—if you know how to use it.
5. What is Hypothesis Testing? - Definition, Steps & Examples
A proper hypothesis test consists of four steps. After watching this video lesson, you'll understand how to create a hypothesis test to help you confirm or disprove an assumption.
6. Conducting Hypothesis Testing for a Mean: Process & Examples
Read this lesson to learn how you can use hypothesis testing to test for a mean. Learn what conditions need to be met before you can use hypothesis testing to find the average for the test subject.
7. The Relationship Between Confidence Intervals & Hypothesis Tests
Quantifying population information by testing a small sample is a marvelous mathematical invention. In this lesson, we explore the relationship between confidence intervals and hypothesis tests.
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Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course
- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards