Question 1
A manufacturer claims that 25% of its customers buy an extended warranty. In a random sample of 200 customers, 62 bought one. For a test of H₀: p = 0.25 against Hₐ: p > 0.25, what are the test statistic and p-value?
AP Statistics formulas, and when to use each
Knowing a formula is half the job. The other half is choosing it: which standard error, which degrees of freedom, which tail.
| Summaries | x̄ = Σx/n, s = √(Σ(x − x̄)²/(n − 1)), z = (x − mean)/SD |
|---|---|
| Probability | P(A or B) = P(A) + P(B) − P(A and B); P(A | B) = P(A and B)/P(B) |
| Inference | statistic ± (critical value)(standard error); test statistic = (statistic − null value)/(standard error) |
| Regression | ŷ = a + bx, b = r(s_y/s_x), residual = y − ŷ |
Unit 1 and Unit 2
- Outlier fences: Q1 − 1.5 × IQR and Q3 + 1.5 × IQR.
- Expected value: E(X) = Σ x·P(x). Standard deviation: √(Σ (x − μ)²·P(x)).
- Binomial: P(X = k) = C(n, k)pᵏ(1 − p)ⁿ⁻ᵏ, mean np, SD √(np(1 − p)).
- Sample mean: mean μ, SD σ/√n. Sample proportion: mean p, SD √(p(1 − p)/n).
Proportions (Unit 3)
- Interval for p: p̂ ± z*√(p̂(1 − p̂)/n). Uses p̂.
- Test for p: z = (p̂ − p₀)/√(p₀(1 − p₀)/n). Uses p₀.
- Interval for p₁ − p₂: each sample's own p̂ in the standard error.
- Test of p₁ = p₂: the pooled p̂ = (x₁ + x₂)/(n₁ + n₂).
- Chi-square: Σ (observed − expected)²/expected, df = (rows − 1)(columns − 1), expected = row total × column total ÷ grand total.
Means (Unit 4)
- One mean or paired differences: t = (x̄ − μ₀)/(s/√n), df = n − 1.
- Two means: SE = √(s₁²/n₁ + s₂²/n₂), with the calculator's degrees of freedom.
- Use t, not z, whenever σ is estimated by s.
Regression (Unit 5)
- The line passes through (x̄, ȳ): a = ȳ − b x̄.
- r² is the fraction of the variation in y explained by the line.
- A residual plot with no pattern supports a linear model.
Try 2 questions
Question 2
For a set of data, x̄ = 20, s_x = 4, ȳ = 50, s_y = 10 and r = 0.6. What is the slope of the least-squares line predicting y from x?
Next step
Questions people ask
Do you get a formula sheet on the AP Statistics exam?
Yes. Formulas and tables are provided on both sections, so the skill tested is choosing the right one and explaining the result.
When do you pool in AP Statistics?
Only in a significance test of p₁ = p₂. Confidence intervals for p₁ − p₂, and every means procedure here, do not pool.