Key Definitions and Results
in
Introductory Statistics

Contents:

Probability

Types of Events

Finding Probabilities

Random Variables and Probability Distributions

Binomial Distribution

Normal Distribution

Sample Statistics and Sampling Distributions

Statistical Inference

Point Estimation

Confidence Intervals

Hypothesis Testing

Probability

Mutually Exclusive Events

Disjoint and Exhaustive Events

Complementary Events

Classical Probability Model

Law of Complementation

General Addition Rule

Theorem of Total Probability

Conditional Probability

Multiplication Rule

Independent Events

Bayes Theorem

Random Variables and Probability Distributions

Cumulative Distribution Function

Binomial PMF

Binomial CDF

Binomial Mean and Variance

Standard Normal PDF

Standard Normal CDF

Standard Normal Quantile (Percentile)

Cumulative Normal Probability

Normal Quantile (Percentile)

Normal Approximation to the Binomial

Sample Statistics and Sampling Distributions

Sample Mean

Sample Variance

Central Limit Theorem (CLT)

Weak Law of Large Numbers (WLLN)

Statistical Inference

Estimation Error

Bias of a Point Estimator

Standard Error

Mean Squared Error

Error Bounds

Consistent Estimator

Confidence Intervals (Two-Sided)

Confidence Interval for a Population Mean

Confidence Interval for a Population Proportion

Confidence Interval for a Population Variance

Confidence Interval for a Difference of Two Means

Confidence Interval for a Difference of Two Proportions

Confidence Interval for a Ratio of Two Variances

Statistical Test of Hypotheses

Type I and Type II Errors

Level of Significance

Power of a Statistical Test

P-Value of a Statistical Test

Testing Hypotheses About a Single Mean

Testing Hypotheses About a Single Proportion

Testing Hypotheses About a Single Variance

Testing Hypotheses About a Difference of Two Means

Testing Hypotheses About a Difference of Two Proportions

Testing Hypotheses About a Ratio of Two Variances

Work in Progress ...