# Ch 36: NYSTCE Mathematics: Sampling & Prediction

### About This Chapter

## NYSTCE Mathematics: Sampling and Prediction - Chapter Summary

This chapter takes you through the role of sampling and prediction in several mathematical operations with the intent to prepare you for related questions on the NYSTCE Mathematics exam. These lessons will address random sampling, the law of large numbers, and chi-square tests. Additionally, by the end of this chapter, you can expect to have strengthened your readiness for questions involving:

- The central limit theorem and sampling distribution
- Interpreting confidence intervals for sample means
- How to determine the sample size to estimate confidence intervals
- Student t distribution
- Using the t distribution to find confidence intervals
- Hypothesis testing
- Relationship between confidence intervals and hypothesis tests
- Properties of algorithms

Each lesson includes both a video and transcript of the content, allowing you to learn the way that fits you best. And after you're through reviewing the lessons, you'll be able to check your comprehension of them with a practice quiz that you can also print as a worksheet to study with offline.

### 1. What is Random Sampling? - Definition, Conditions & Measures

Random sampling is used in many research scenarios. In this lesson, you will learn how to use random sampling and find out the benefits and risks of using random samples.

### 2. Understanding the Law of Large Numbers

The law of large numbers is a concept that is often misunderstood in statistics. In this lesson, you will learn the real meaning of the law of large numbers and how it is employed.

### 3. Sampling Distributions & the Central Limit Theorem: Definition, Formula & Examples

Want proof that all of this normal distribution talk actually makes sense? Then you've come to the right place. In this lesson, we look at sampling distributions and the idea of the central limit theorem, a basic component of statistics.

### 4. 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.

### 5. Finding Confidence Intervals with the Normal Distribution

In this lesson, you're going to learn how to construct a confidence interval when the population's standard deviation is known and the population is normally distributed.

### 6. 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.

### 7. Student t Distribution: Definition & Example

In this lesson, you're going to learn about the t-distribution, t-curves, their important properties, and differences from the standard normal distribution as well as how to find the value of t.

### 8. Using the t Distribution to Find Confidence Intervals

In this lesson, you're going to learn how we find confidence intervals for normally distributed populations where the population standard deviation is not known. Work through the sample, then test your understanding with a brief quiz.

### 9. What is a Chi-Square Test? - Definition & Example

This lesson explores what a chi-square test is and when it is appropriate to use it. Using a simple example, we will work on understanding the formula and how to calculate the p-value.

### 10. 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.

### 11. 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.

### 12. Effect Size in Hypothesis Testing: Definition & Interpretation

Watch this video lesson to learn what effect size is when used in hypothesis testing. Also learn what significance it has in your testing. Learn how your data affects the effect size.

### 13. Type I & Type II Errors in Hypothesis Testing: Differences & Examples

Watch this video lesson to learn about the two possible errors that you can make when performing hypothesis testing. You will see how important it is to really understand what these errors mean for your results.

### 14. 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.

### 15. Properties of Algorithms

Algorithms are a set of step-by-step instructions that satisfy a certain set of properties. In this lesson, we'll explore the properties an algorithm must satisfy in order to be useful using an example.

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### Other Chapters

Other chapters within the NYSTCE Mathematics (004): Practice & Study Guide course

- NYSTCE Mathematics: Fractions, Decimals & Percents
- NYSTCE Mathematics: Complex Numbers
- NYSTCE Mathematics: Factoring & Divisibility
- NYSTCE Mathematics: Exponents
- NYSTCE Mathematics: Patterns & Functions
- NYSTCE Mathematics: Understanding Algebraic Expressions
- NYSTCE Mathematics: Solving Algebraic Equations
- NYSTCE Mathematics: Linear Equations
- NYSTCE Mathematics: Quadratic Functions
- NYSTCE Mathematics: Polynomial Functions
- NYSTCE Mathematics: Exponential Expressions
- NYSTCE Mathematics: Absolute Value Expressions
- NYSTCE Mathematics: Rational Expressions
- NYSTCE Mathematics: Radical Expressions
- NYSTCE Mathematics: Exponential & Logarithmic Functions
- NYSTCE Mathematics: Trigonometry
- NYSTCE Mathematics: Applications of Trigonometry
- NYSTCE Mathematics: Calculus Concepts
- NYSTCE Mathematics: Calculus Applications
- NYSTCE Mathematics: Principles of Measurement
- NYSTCE Mathematics: Lines & Angles
- NYSTCE Mathematics: Parallel Lines & Symmetry
- NYSTCE Mathematics: Geometric Construction
- NYSTCE Mathematics: Geometric Shapes
- NYSTCE Mathematics: Triangle Proofs & Theorems
- NYSTCE Mathematics: Geometric Solids
- NYSTCE Mathematics: Conic Sections
- NYSTCE Mathematics: Vector Operations
- NYSTCE Mathematics: Transformations in Geometry
- NYSTCE Mathematics: Coordinate Geometry
- NYSTCE Mathematics: Sequences & Series
- NYSTCE Mathematics: Counting Strategies
- NYSTCE Mathematics: Probability
- NYSTCE Mathematics: Probability Distributions
- NYSTCE Mathematics: Data Analysis & Statistics
- NYSTCE Mathematics: Regression & Correlation
- NYSTCE Mathematics: Discrete Mathematics
- NYSTCE Mathematics Flashcards