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Confidence vs Significance Levels: Critical Values Explained

AP Statistics: Master Data Analysis & Probability

Basic Concepts

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Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Census and bias

Census and Bias

Classifying Bias

Data Representation

Frequency distribution and histograms

Frequency polygons

Shapes of distributions

Data Interpretation

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Bivariate, scatter plots and correlation 

Regression analysis

Equation of the best fit line

Probability

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability with permutations and combinations

Probability involving permutations and combinations

Law of total probability

Law of Total Probability

Probability of a randomly selected employee meeting a sales target

Probability of a randomly selected driver being involved in an accident

Probability of a randomly selected customer making a purchase

Probability of a randomly selected person being overweight

Bayes' rule

Bayes" Rule

Bayes rule

Bayes" rule

Bayes' Rule

Discrete Probabilities

Probability distribution - histogram, mean, variance & standard deviation

Binomial distribution

Binomial Distribution

Mean and standard deviation of binomial distribution

Interpreting Mean and Standard Deviation of Binomial

Geometric distribution

Hypergeometric distribution

Determining the Cumulative Hypergeometric Distribution

Hypergeometric Distribution

Properties of expectation

Properties of Expectation and Variance

Properties of Expectation

Normal Distribution and Z-Scores

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

Sampling distributions

Understanding Proportions and Sample Size

Central limit theorem

Central Limit Theorem

Applying the Central Limit Theorem

Rare event rule

The Rare Event Rule for the Central Limit Theorem

Confidence Intervals

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Chi-Squared confidence intervals

Chi-Squared Confidence Intervals

Confidence intervals to estimate population mean

Student's t-distribution

Student"s t-distribution

Determining a Confidence Interval for a Population Mean using t-distributions

Hypothesis Testing

Null hypothesis and alternative hypothesis

Proving claims

Confidence levels, significance levels and critical values

Test statistics

Traditional hypothesis testing

Traditional Mean Hypothesis Testing

P-value hypothesis testing

Proportion Hypothesis Testing

Mean hypothesis testing with t-distribution

Hypothesis Testing Mean Claims without Knowing <katex> \sigma </katex>

Chi-square goodness of fit test

Type 1 and type 2 errors

Type 1 and Type 2 Errors

Set Theory

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

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Aligning with the <a href="https://apstudent.collegeboard.org/apcourse/ap-statistics">AP Statistics curriculum</a> by College Board, our comprehensive statistics help covers content in all four major themes including Exploring data; Sampling and Experimentation; Anticipating patterns using probability and simulation; and Statistical inference. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest statistics problems. Then, strengthen your understanding with tons of ap stats practice questions.

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AP Statistics

sample

math

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-APstatistics.png

Ex.1

Ex.2

Ex.3

Rejecting the null hypothesis using a critical value and z score

Ex.4

Left-tail hypothesis test for population mean at 95% confidence

Ex.5

Hypothesis test on Canadian pet ownership using a two-tailed z-test

intro

Intro to confidence levels, significance levels, and critical values

Finding the critical value for a right-tail test at 0.075 significance

Finding the critical value for a left tail test

Finding critical values for a two-tail test with alpha 0.075

Finding the critical z-value for a right tail test at 90% confidence

Finding the critical value for a 95% confidence right tail test

Finding the critical value for a right-tailed test at 99% confidence

Confidence levels, significance levels, and critical values

Understanding confidence and significance levels

Understanding Confidence and Significance Levels in Statistics

What You'll Learn

Convert between significance levels and confidence levels using the relationship α + (1-α) = 1

Identify rejection and fail-to-reject regions on the standard normal distribution

Determine critical values for left-tail, right-tail, and two-tail hypothesis tests

Apply critical values to decide whether to reject or fail to reject a null hypothesis

What You'll Practice

Finding critical values for given confidence levels (90%, 95%, 99%)

Drawing standard normal curves with rejection regions for different tail tests

Comparing test statistics to critical values to make hypothesis decisions

Working with two-tail tests by splitting significance levels in half

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

10 Video lessons

Practice exercises

Learning resources

Skills

Confidence Levels

Significance Levels

Critical Values

Hypothesis Testing

Standard Normal Distribution

Z-scores

Rejection Regions

Two-tail Tests