AP Statistics Cheat Sheet Summary

General Tips

• B.S.: Be Specific; include numbers where possible and refer back to the context of the problem.
• Define what you're discussing and show your work.
• Read the entire question first; ask what the question is about.
• Check your answer to ensure it makes sense.

Describing/Comparing Distributions

• Center: Median or mean.
• Unusual Features: Gaps or outliers.
• Spread: Interquartile range (IQR), standard deviation, or range.
• Shape: Symmetrical, bimodal, or skewed.

Binomial Distribution

• Binary: Success or failure.
• Independent: Trials are independent.
• Number of Trials: Fixed.
• Success Probability: Stays the same.

Defining a Binomial Distribution

• X has a binomial distribution with parameters n and p.

Geometric Distribution

• Binary: Success or failure.
• Independent: Trials are independent.
• Trials: Until success.
• Success Probability: Stays the same.

Defining a Geometric Distribution

• X has a geometric distribution with parameter p.

Constructing a Confidence Interval

• P: Define parameters, including confidence level.
• A: State assumptions/conditions.
• N: Name the interval.
• I: Calculate the interval.
• C: State the conclusion in context.

Performing a Hypothesis Test

• P: Define parameters, including significance level.
• H: Write your hypotheses.
• A: State assumptions/conditions.
• N: Name the test.
• T: Calculate the test statistic.
• O: Obtain the p-value.
• M: Make a decision.
• S: State the conclusion in context.

Describing a Relationship

• STD: Uses correlation coefficient, r.
  • S: Strength - strong, moderate, or weak.
  • T: Trend - linear or nonlinear.
  • D: Direction - positive or negative.

Describing a Scatterplot

• D: Direction - positive or negative.
• U: Unusual features - outliers.
• F: Form - linear or nonlinear.
• S: Strength - strong, moderate, or weak.

Sentence Stems

• Slope: As x-variable increases by 1 unit, predicted y-variable changes by slope units.
• Y-intercept: When x-variable is 0, predicted y-variable is the y-intercept.
• Relationship: There is a strength, trend, direction relationship between x and y based on graph or r.
• Coefficient of Determination (R^2): Percentage of variability in y explained by x.
• Mean: Average context will be about mean value.
• Standard Deviation: Context typically varies from mean by SD value.
• Confidence Interval: We are X% confident the true parameter is between the bounds in context.
• Confidence Level: X% of intervals would capture true parameter if many intervals constructed.
• P-value: Chance of getting a sample mean/proportion as extreme as the observed, assuming H0 is true.
  • Fail to Reject H0: No convincing evidence for Ha.
  • Reject H0: Convincing evidence for Ha.
• Power: Probability of finding evidence to reject H0 if Ha is true.

Inference Table

• 1 Proportion z
  • Random: Sample must be randomly selected or assigned.
  • Independence: Sample size < 10% of population.
  • Normality: np and n(1-p) > 10.
• 2 Proportion z
  • Check both samples for random selection, independence, and normality.
• 1 Sample t
  • Random, independent, normality (no unusual features or n > 30).
• 2 Sample t
  • Check both samples for random selection, independence, and normality.

Proportions vs. Means

• Proportions: Categorical data, Yes/No answers, data as fractions.
• Means: Quantitative data, numerical answers.

Random Formulas

• Various mathematical transformations and combinations of means and standard deviations.

General Things to Remember

• Graph Labeling: Title, label axes, and scale.
• PDF vs CDF: PDF for specific probabilities, CDF for ranges.
• Independence Check: P(A) = P(A|B).
• Type I and Type II Errors: Power of a test.
• Use normalcdf and invNorm functions for probability calculations.