AP Statistics Lecture Notes

Introduction

• AP Statistics overview
• Importance of understanding key statistics concepts
• Video structure includes chapter overviews and specific AP exam weightings

Chapter 1: Statistical Studies

Section 1: Definitions

• Statistics: Collecting, organizing data, making generalizations to populations
• Key Terms:
  • Population: Large group of interest
  • Sample: Subset of the population
  • Statistical Unit: A member of the sample
  • Population Parameter: Number describing the population
  • Descriptive Statistic: Describes a sample

Types of Statistical Studies

• Observational Study: Observes without affecting behavior
• Experiment: Involves treatment assignment
• Variables:
  • Explanatory (Independent) Variable: Variable adjusted
  • Response (Dependent) Variable: Measured outcome
  • Confounding Variable: Unaccounted variable affecting both explanatory and response variables

Experimental Designs

• Control: Accounting for confounding variables
• Designs:
  • Completely Randomized Design
  • Randomized Block Design
  • Matched Pairs Design

Blinding and Placebo

• Double-Blind: Subjects and observers unaware of treatment assignments
• Single-Blind: Only subjects or observers are unaware
• Placebo Effect: Inactive treatment causes effect due to expectations

Correlation vs Causation

• Correlation: Trend between variables
• Causation: One variable causes changes in another
• Importance of acknowledging confounding variables

Miscellaneous Terms

• Replication: Consistency of results
• Census: Observing an entire population

Sampling and Bias

• Sampling Methods:
  • Simple Random Sampling, Systematic Sampling, Stratified Random Sampling, Cluster Sampling, Convenience Sampling
• Types of Bias:
  • Sampling Bias, Undercoverage Bias, Response Bias, Non-response Bias, Voluntary Response Bias

Data Visualization

• Histograms, Dot Plots, Pie Charts
• Box Plots: Visualization with outliers
• Descriptive Statistics: Mean, Variance, Standard Deviation, Range

Distribution Shapes

• Discrete vs Continuous Variables
• Normal Distribution: Bell curve properties

Chapter 2: Statistical Inference

Confidence Intervals

• Example Problem: Calculating 95% confidence interval
• Steps:
  • Check required conditions
  • Calculate using point estimate ± margin of error

Hypothesis Testing

• Four Steps:
  1. Set up test and conditions
  2. Obtain a z-statistic
  3. Calculate p-value
  4. Determine results
• Errors: Type 1 and Type 2 errors

Sampling Distribution for Two Proportions

• Formulas for Means and Standard Deviations
• Confidence Interval and Hypothesis Testing

T Distributions for Population Mean

• Central Limit Theorem
• T vs Z Distribution
• Confidence Intervals and Hypothesis Testing for means

Linear Regression

• Describing Bivariate Relationships
• Least Squares Linear Regression
• Correlation Coefficient (R) and Coefficient of Determination (R²)

Linear Regression Inference

• Conditions for Linear Regression
• Confidence Interval and Hypothesis Testing for slope

Graphing Calculator Use

• Tests and Intervals
• Probability Density Functions

Chapter 3: Probability

Probability Rules

• Important Notations: Intersection, Union, Complement
• Product Rule: For independent events
• Sum Rule: For mutually exclusive events

Tables

• One-way and Two-way Tables
• Conditional, Marginal, Joint Probability
• Independence Determination

Chi-square Tests

• Goodness of Fit, Independence, Homogeneity
• Steps for Chi-square Tests

Binomial and Geometric Probability

• Binomial Probability: Fixed number of trials
• Geometric Probability: First success on x-th trial

Graphing Calculator for Probability

• Chi-square Tests and Binomial/Geometric Calculations

Conclusion

• Encouragement to review and ask questions
• Note that these concepts will be foundational for AP Statistics success