Night-Before Essentials | Mr. Levy AP Stats

✅ Conditions for Every Test — Exact FRQ Language

Write these out in full on every FRQ. Skipping or shortcutting conditions is the #1 way to lose points.

Procedure	Random	10% Condition	Normal / Large Counts
1-Prop Z Test 1-Prop Z Interval	✓ The data come from a random sample or random assignment.	✓ n ≤ 10% of the population.	✓ n·p₀ ≥ 10 and n·(1−p₀) ≥ 10. (Use p₀ for tests; use p̂ for intervals)
2-Prop Z Test 2-Prop Z Interval	✓ Random sample or random assignment for each group.	✓ n₁ ≤ 10% of pop. 1 and n₂ ≤ 10% of pop. 2.	✓ n₁p̂₁ ≥ 10, n₁(1−p̂₁) ≥ 10 and n₂p̂₂ ≥ 10, n₂(1−p̂₂) ≥ 10.
1-Sample T Test 1-Sample T Interval	✓ The data come from a random sample or random assignment.	✓ n ≤ 10% of the population.	✓ n ≥ 30 (CLT), OR population is Normal, OR sample graph shows no strong skew or outliers (for small n).
2-Sample T Test 2-Sample T Interval	✓ Random sample or random assignment for each group.	✓ n₁ ≤ 10% of pop. 1 and n₂ ≤ 10% of pop. 2.	✓ Each group: n ≥ 30, OR approx. Normal distribution.
Paired T Test Paired T Interval	✓ The pairs come from a random sample or random assignment.	✓ n ≤ 10% of the population.	✓ n ≥ 30, OR the differences are approximately Normal (check graph).
χ² Goodness of Fit	✓ The data come from a random sample.	✓ n ≤ 10% of the population.	✓ All expected counts ≥ 5.
χ² Homogeneity	✓ Random sample from each population being compared.	✓ Each sample ≤ 10% of its population.	✓ All expected counts ≥ 5.
χ² Independence	✓ The data come from a random sample.	✓ n ≤ 10% of the population.	✓ All expected counts ≥ 5.
Regression T Test (slope β)	✓ Random sample or randomized experiment.	Not required	✓ LINER — check the residual plot: Linear (no curve), Independent observations, Normal residuals, Equal variance (no fan shape), Random.

💡 Expected count formula for χ²: (row total × column total) / grand total

✍️ FRQ Conclusion Templates

Fill in the blanks. Always restate the finding in context — generic conclusions lose points every time.

Significance Test — Reject H₀

Because the p-value ( ) < α = , we reject H₀. There is convincing evidence that [restate Hₐ in context].

Significance Test — Fail to Reject H₀

Because the p-value ( ) ≥ α = , we fail to reject H₀. We do not have convincing evidence that [restate Hₐ in context].

Confidence Interval — Interpretation

We are % confident that the true [parameter name in context] is between and .

Confidence Interval — Used as a Decision

Because [is / is not] contained in the interval, we [do / do not] have convincing evidence that [Hₐ in context].

Chi-Square — Reject H₀ (Independence)

Because the p-value ( ) < α = , we reject H₀. There is convincing evidence of an association between [variable 1] and [variable 2].

Chi-Square — Reject H₀ (Homogeneity)

Because the p-value ( ) < α = , we reject H₀. There is convincing evidence that the distribution of [variable] differs across [the populations].

Regression — Reject H₀ (slope)

Because the p-value ( ) < α = , we reject H₀: β = 0. There is convincing evidence of a linear relationship between [x variable] and [y variable].

Regression — CI for Slope Interpretation

We are % confident that for each additional [one unit of x], the true mean [y in context] changes by between and .

⚠️ Never write "accept H₀" — always "fail to reject H₀." And never say "prove" — say "convincing evidence."

🚨 The 5 Mistakes That Cost the Most Points

These show up every year. Knowing them is free points.

1

Incomplete or missing conditions

You must check all three conditions (Random, 10%, Normal/Large Counts) for every inference procedure. Stating the name of a condition without verifying it with numbers doesn't get full credit. Show the work: write np₀ = ___ ≥ 10.
2

Writing "accept H₀" instead of "fail to reject H₀"

You never accept the null — you only fail to find convincing evidence against it. "Fail to reject H₀" is the required phrasing. This is an automatic point deduction on any FRQ conclusion.
3

No context in the conclusion

"Reject H₀" alone is never enough. The conclusion must reference the variables and population from the problem. Use the templates above — they force context into every sentence.
4

Using p₀ instead of p̂ in the standard error for a 2-proportion interval

For a test, use p̂꜀ (pooled) in the SE. For an interval, use p̂₁ and p̂₂ (the sample proportions) — not the null value p₀. Mixing these up is one of the most common calculation errors.
5

Subtracting standard deviations instead of adding variances

When combining two independent random variables: Variances add, standard deviations do not. σ²(X−Y) = σ²X + σ²Y → then take the square root. Never write σ(X−Y) = σX − σY.

You've put in the work all year. Tonight, review these conditions once, glance at the templates, and get some sleep. Tomorrow afternoon, walk in, read carefully, write in context, and trust yourself.

— Mr. Levy

📋 Night-Before Essentials

✅ Conditions for Every Test — Exact FRQ Language

✍️ FRQ Conclusion Templates

🚨 The 5 Mistakes That Cost the Most Points