Statistics Final Exam Cheat Sheet

This cheat sheet provides a structured approach to solving statistics problems, focusing on identifying question types, selecting appropriate tests, checking conditions, and interpreting results correctly for high exam scores.

Core Principles

Always start by identifying the type of question: successes (Binomial), mean (z/t test), proportion (z test), confidence interval, or normal distribution.
Understand the conditions required for each test (Random, Normal/n≥30 for means; Random, np≥10, n(1-p)≥10 for proportions).
Know the formulas for test statistics (z and t) and confidence intervals for means and proportions.
Master hypothesis testing steps: State hypotheses, check conditions, calculate test statistic, find p-value, make a decision, and conclude in context.
Differentiate between one-tailed (>, <) and two-tailed (≠) tests based on the wording.
Understand the p-value as the probability of observing results as extreme as, or more extreme than, the observed results, assuming the null hypothesis is true.

Action Steps

1. Identify the question type (mean, proportion, etc.).
2. Determine the correct test (z-test, t-test, binomial).
3. Verify all necessary conditions are met.
4. Calculate the test statistic and p-value.
5. Apply the decision rule (p ≤ α).
6. State the conclusion clearly in the context of the problem.

Formulas

$z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$
$t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$
$z = \frac{\hat{p} - p}{\sqrt{p(1-p)/n}}$
$\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$
$\bar{x} \pm t^* \frac{s}{\sqrt{n}}$
$\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$
$ME = (critical)(SE)$
$P(X=x) = \binom{n}{x} p^x (1-p)^{n-x}$
$z = (x - \mu)/\sigma$
$IQR = Q3 - Q1$
$Lower Outlier Bound = Q1 - 1.5(IQR)$
$Upper Outlier Bound = Q3 + 1.5(IQR)$
$P(A|B) = P(A \cap B) / P(B)$

Key Terms

Null Hypothesis (H₀): A statement of no effect or no difference.
Alternative Hypothesis (Hₐ): A statement that contradicts the null hypothesis.
p-value: Probability of observing data as extreme or more extreme than the sample data, assuming H₀ is true.
Significance Level (α): The threshold for rejecting the null hypothesis (commonly 0.05).
Type I Error: Rejecting a true null hypothesis (false positive).
Type II Error: Failing to reject a false null hypothesis (false negative).
Statistical Significance: A result that is unlikely to have occurred by random chance alone (small p-value).
Practical Significance: A result that has a meaningful impact in the real world.
Parameter: A numerical characteristic of a population (e.g., μ, p).
Statistic: A numerical characteristic of a sample (e.g., x̄, p̂).
IQR: Interquartile Range (Q3 - Q1), a measure of spread.

Pro Tips

The p-value is NOT the probability that the null hypothesis is true.
Always translate conclusions back into the context of the problem.
The reverse logic for decision rules (Fail = p > α, Reject = p ≤ α) is a powerful shortcut.
Increase sample size (n) to decrease margin of error and increase power.
IQR is the most important measure of spread for skewed data or data with outliers.

Pitfalls to Avoid

Confusing parameters (population, Greek letters) with statistics (sample, Roman letters).
Misinterpreting the p-value as the probability of the null hypothesis being true.
Forgetting to check conditions before performing a test.
Failing to state the conclusion in the context of the original problem.
Confusing statistical significance with practical significance.