AP stat conditions

1. One-sample z interval (proportion)

  • Random: data from a random sample or randomized experiment

  • 10% condition: sample ≤ 10% of population (if sampling without replacement)

  • Success–Failure:

    • np^≥10np̂ ≥ 10np^​≥10 and n(1−p^)≥10n(1 - p̂) ≥ 10n(1−p^​)≥10

2. One-sample z test (proportion)

  • Random

  • 10% condition

  • Success–Failure (use null proportion p0p₀p0​):

    • np0≥10np₀ ≥ 10np0​≥10 and n(1−p0)≥10n(1 - p₀) ≥ 10n(1−p0​)≥10

3. Two-sample z interval (difference in proportions)

  • Random for both samples

  • Independent groups (or randomized assignment)

  • 10% condition for both samples

  • Success–Failure (use sample proportions):

    • n1p^1≥10n₁p̂₁ ≥ 10n1​p^​1​≥10, n1(1−p^1)≥10n₁(1-p̂₁) ≥ 10n1​(1−p^​1​)≥10

    • n2p^2≥10n₂p̂₂ ≥ 10n2​p^​2​≥10, n2(1−p^2)≥10n₂(1-p̂₂) ≥ 10n2​(1−p^​2​)≥10

4. Two-sample z test (difference in proportions)

  • Same as above, BUT:

  • Success–Failure uses pooled proportion p^p̂p^​:

    • n1p^≥10n₁p̂ ≥ 10n1​p^​≥10, n1(1−p^)≥10n₁(1-p̂) ≥ 10n1​(1−p^​)≥10

    • n2p^≥10n₂p̂ ≥ 10n2​p^​≥10, n2(1−p^)≥10n₂(1-p̂) ≥ 10n2​(1−p^​)≥10

📊 T procedures for means

5. One-sample t interval (mean)

  • Random

  • 10% condition

  • Normal/Large Sample:

    • population is normal OR

    • sample size ≥ 30 OR

    • no strong skewness/outliers

6. One-sample t test (mean)

  • Same conditions as above:

    • Random

    • 10% condition

    • Normal/Large sample

7. Paired t interval / test

  • Random

  • 10% condition

  • Work with differences

  • Normal/Large Sample on differences:

    • differences are approximately normal

    • or n≥30n ≥ 30n≥30

8. Two-sample t interval (difference in means)

  • Random for both samples

  • Independent groups

  • 10% condition for both

  • Normal/Large Sample for both groups:

    • each group roughly normal OR

    • both sample sizes ≥ 30 OR

    • no strong skew/outliers

9. Two-sample t test (difference in means)

  • Same as interval:

    • Random

    • Independent

    • 10% condition

    • Normal/Large Sample

📈 Regression (slope)

10. t interval for a slope / t test for slope

Use LINE conditions:

  • L (Linear): relationship is linear

  • I (Independent): observations independent

  • N (Normal): residuals approximately normal

  • E (Equal variance): constant variance (no funnel shape)

🧮 Chi-square (χ² tests)

11. Chi-square goodness of fit

  • Random

  • 10% condition

  • Large counts:

    • all expected counts ≥ 5

12. Chi-square test for homogeneity

  • Random

  • Independent groups

  • 10% condition

  • Large counts:

    • all expected counts ≥ 5

13. Chi-square test for independence

  • Random

  • 10% condition

  • Large counts:

    • all expected counts ≥ 5