How much detail do I need when checking conditions on an FRQ?

You need to name each condition, reference the specific context or plug in the actual numbers, and state that it is satisfied. For example, write 'np = 250(0.66) = 165 ≥ 10' rather than just 'Large Counts ✓.' Vague checkmarks or symbolic inequalities without values typically do not earn full credit.

Should I use p or p_0 when checking Large Counts?

For a confidence interval, use the sample proportion p because there is no hypothesized value. For a significance test, use the null value p_0, since the test operates under the assumption that H_0 is true. For a two-proportion test, use the pooled proportion. Mixing these up is one of the most common Unit 6 errors.

Can I just use my calculator's test function without showing the formula?

You can use calculator output for the computation, but you must still name the procedure, check conditions, report the test statistic and p-value (or interval endpoints), and write a conclusion in context. Reporting only calculator output with no supporting work risks losing method points. Naming the procedure, like 'one-proportion z-test,' is essential.

How do I answer a part that says 'use your confidence interval' to make a decision?

Do not run a separate significance test. Instead, check whether the null value (or 0 for a difference of proportions) falls inside the interval. If the null value is not in the interval, that is evidence against it at the corresponding significance level; if it is inside, you lack convincing evidence of a difference. Then state your conclusion in context.

AP-STATS-6-FRQ

U6 FRQ Practice

Master Unit 6 AP Statistics FRQs on proportions: how to structure confidence-interval and significance-test responses to earn every point on the exam.

What you'll do in this lesson

A voice-first session with the Crimsora tutor on U6 FRQ Practice, then targeted practice and FRQs — with the tutor adapting to where you get stuck.

Start U6 FRQ Practice free

What this lesson covers

Unit 6 free-response questions are where the AP Statistics exam checks whether you can actually carry out inference for proportions, not just recognize a formula. Graders use a rubric with clearly defined "parts" — and students routinely lose points not because their statistics are wrong, but because they skip a condition, forget to define a parameter, or state a conclusion that doesn't connect back to the context.

This lesson is pure FRQ strategy. We assume you already know the mechanics of one- and two-proportion intervals and tests (those live in the neighboring lessons). Here you'll learn the four-step template graders expect, the phrases that earn credit, the traps that cost it, and how to read a prompt to decide which procedure to run.

The Four-Step Template That Earns Points

Almost every Unit 6 inference FRQ is scored against a four-step structure. Memorize it and apply it every single time, whether you are building a confidence interval or running a test.

Step	What graders look for	Common phrase
State	Name the procedure and define parameters in context	"Let $p$ = the true proportion of..."
Plan	Name conditions and check them with the actual numbers	"Random, $10\%$ , Large Counts"
Do	Compute the interval or test statistic and p-value	$z = \frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$
Conclude	Interpret in context, tied to the question asked	"Because p-value $<\alpha$ , we reject $H_0$ ..."

The biggest scoring mistake is jumping straight to "Do." A perfect calculation with no stated procedure and no checked conditions often earns only partial credit. Conversely, students who write out State–Plan–Do–Conclude clearly frequently pick up points even when arithmetic slips, because rubrics award a correct method separately from a correct value.

Write in complete sentences where interpretation is required. The exam is not a scratch pad; graders reward communication.

Choosing the Right Procedure

Before writing anything, decide which Unit 6 tool the prompt demands. Misidentifying the procedure usually zeros the whole part.

Prompt signal	Procedure
"Estimate," "how confident," "margin of error," one group	One-proportion $z$ -interval
"Is there evidence," "test the claim," one group vs. a fixed value	One-proportion $z$ -test
"Estimate the difference" between two groups	Two-proportion $z$ -interval
"Is there a difference," comparing two groups	Two-proportion $z$ -test

Watch the number of samples. If the data describe two independent groups (treatment vs. control, men vs. women), you need a two-proportion method. A single sample compared to a benchmark ("more than 60%") signals a one-proportion method.

Also note the difference between a test and an interval. A test asks whether an effect exists and produces a decision; an interval estimates a plausible range for the parameter. If a later part of the FRQ asks you to "use your interval" to make a decision, remember that an interval containing 0 (for a difference) or the null value means no significant difference at the corresponding significance level.

Conditions: The Points Everyone Leaves on the Table

Checking conditions is the most predictable source of lost points. You must (1) name the condition, (2) reference the specific context or numbers, and (3) state that it is met.

The Random condition requires that data come from a random sample or randomized experiment — quote the prompt ("the students were randomly selected"). Do not just write "random ✓."

The $10\%$ condition applies when sampling without replacement:

n \le 0.10N

. State it in context, e.g. "It is reasonable to assume there are more than

10(200) = 2000

voters in the town."

The Large Counts condition differs between intervals and tests. For a one-proportion interval, check

n\hat{p} \ge 10

and

n(1-\hat{p}) \ge 10

using

\hat{p}

. For a one-proportion test, use the null value

p_0

np_0 \ge 10

and

n(1-p_0) \ge 10

. For two-proportion tests, use the combined (pooled) proportion. Mixing these up is a classic error.

Actually plug in numbers: "

n\hat{p} = 150(0.42) = 63 \ge 10

." Writing the inequality symbolically without the arithmetic is not full credit.

Writing Conclusions That Don't Lose Points

Conclusions are graded strictly for correct logic and context. For a significance test, always compare the p-value to

\alpha

(state

\alpha = 0.05

if none is given), make a decision about

H_0

, and answer the original question in context.

A full-credit conclusion: "Because the p-value of

0.017

is less than

\alpha = 0.05

, we reject

H_0

. There is convincing evidence that the true proportion of defective parts exceeds

0.10

."

Common errors: "accepting" the null (you never accept

H_0

— you fail to reject it), forgetting the context, and drawing a causal conclusion when the study was observational. Only randomized experiments justify cause-and-effect language.

For confidence intervals, the interpretation of the interval and the interpretation of the confidence level are different and both get tested. Interval: "We are 95% confident that the true difference in proportions is between

0.02

and

0.14

." Confidence level: "If we repeated this sampling process many times, about 95% of the resulting intervals would capture the true parameter." Never say there is a 95% probability the parameter lies in your specific interval — that phrasing loses the point.

Managing the Multi-Part FRQ

Unit 6 FRQs often have parts (a), (b), (c) that build on each other. Read all parts before starting so you know where the question is heading. A part might ask you to construct an interval, then a later part asks you to "use the interval" to address a claim — meaning you should not run a separate test; you should reason from the interval.

Manage your time: roughly 12–13 minutes per full FRQ. Do not over-write. If asked only to "interpret the p-value," give exactly that: "Assuming

H_0

is true, there is a

0.017

probability of getting a sample result at least as extreme as the one observed." Interpreting a p-value is a frequently tested and frequently missed micro-skill.

If a part asks about a possible error, connect it to context: a Type I error means concluding an effect exists when it truly does not; a Type II error means missing a real effect. Describe the real-world consequence when asked. Finally, if you get stuck on the arithmetic in one part, still write your conclusion structure — you may earn the interpretation point using whatever value you computed.

Key terms

Parameter.: The true population quantity you are estimating or testing, such as $p$ (one proportion) or $p_1 - p_2$ (difference of proportions). Must be defined in context in the State step.
Large Counts Condition.: The requirement that expected successes and failures each be at least 10. Uses $\hat{p}$ for intervals but the null value $p_0$ (or the pooled proportion for two-sample tests) for tests.
Pooled Proportion.: The combined sample proportion $\hat{p}_c = \frac{X_1 + X_2}{n_1 + n_2}$ used to compute the standard error in a two-proportion $z$ -test (not in the interval).
p-value.: The probability, assuming $H_0$ is true, of observing a sample statistic at least as extreme as the one obtained. Compared against $\alpha$ to make a decision.
Type I Error.: Rejecting a true null hypothesis — concluding an effect exists when it does not. Its probability equals $\alpha$ .
Type II Error.: Failing to reject a false null hypothesis — missing a real effect. Its probability is denoted $\beta$ .
Confidence Level Interpretation.: A statement about the long-run capture rate of the method: in repeated sampling, this percentage of intervals would contain the true parameter.
Statistical Significance.: The condition that a p-value is smaller than $\alpha$ , providing convincing evidence against the null hypothesis.

Worked example

A researcher wants to know whether more than 60% of a large city's residents support a new bike-lane project. In a random sample of 250 residents, 165 said they support it. Perform an appropriate test at the

\alpha = 0.05

level and state your conclusion.

State: Let

p

= the true proportion of all residents in the city who support the bike-lane project.

H_0: p = 0.60

versus

H_a: p > 0.60

. This is a one-proportion

z

-test.

Plan: Check conditions. Random: the residents were a random sample, so this is met.

10\%

: it is reasonable that there are more than

10(250) = 2500

residents in a large city. Large Counts (use

p_0 = 0.60

np_0 = 250(0.60) = 150 \ge 10

and

n(1-p_0) = 250(0.40) = 100 \ge 10

. All conditions are met.

Do: The sample proportion is

\hat{p} = \frac{165}{250} = 0.66

. The test statistic is

z = \frac{0.66 - 0.60}{\sqrt{\frac{0.60(0.40)}{250}}} = \frac{0.06}{0.03098} \approx 1.94.

For a right-tailed test, the p-value is

P(Z > 1.94) \approx 0.026

.

Conclude: Because the p-value of

0.026

is less than

\alpha = 0.05

, we reject

H_0

. There is convincing evidence that more than 60% of the city's residents support the bike-lane project.

Practice questions

A significance test for a proportion gives a p-value of 0.08 at

\alpha = 0.05

. Which conclusion is written correctly?

Because $0.08 > 0.05$ , we accept $H_0$ and conclude there is no effect.
Because $0.08 > 0.05$ , we fail to reject $H_0$ ; there is not convincing evidence of an effect.
Because $0.08 > 0.05$ , we reject $H_0$ ; there is convincing evidence of an effect.
Because $0.08 > 0.05$ , there is a 92% probability the null hypothesis is true.

Answer: Because $0.08 > 0.05$ , we fail to reject $H_0$ ; there is not convincing evidence of an effect.

When the p-value exceeds

\alpha

, we fail to reject the null hypothesis — we never "accept" it, since failing to find evidence is not proof of no effect. The p-value is also not the probability that

H_0

is true. Only the second option uses correct decision language and correct interpretation.

A study compares the proportion of two independent groups that recover using treatment A versus treatment B. Explain how to decide whether to use a two-proportion z-test or a two-proportion z-interval, and describe one condition that must be checked differently for the test than for the interval.

Answer: Use the test if the question asks whether a difference exists; use the interval if it asks to estimate the size of the difference. The Large Counts condition uses the pooled proportion for the test but each group's own $\hat{p}$ for the interval.

The wording of the prompt determines the procedure: 'is there a difference' or 'is there evidence' signals a test producing a decision, while 'estimate the difference' signals an interval. For the two-proportion test, expected counts are checked with the pooled (combined) proportion

\hat{p}_c

because

H_0

assumes the proportions are equal; for the interval there is no assumed common value, so each sample proportion is used to check counts. Recognizing this distinction is a frequent FRQ scoring point.

In the worked example above, interpret the meaning of the p-value of 0.026 in context.

Answer: Assuming the true proportion of supporters is exactly 0.60, there is about a 0.026 probability of obtaining a sample proportion of 0.66 or higher from a random sample of 250 residents.

A p-value interpretation must include three elements: the assumption that

H_0

is true, the phrase 'at least as extreme' (here, 0.66 or higher because it is a right-tailed test), and reference to the sample context. Simply saying 'the probability the null is true is 0.026' would be incorrect and would lose the point.

FAQ

How much detail do I need when checking conditions on an FRQ?: You need to name each condition, reference the specific context or plug in the actual numbers, and state that it is satisfied. For example, write ' $n\hat{p} = 250(0.66) = 165 \ge 10$ ' rather than just 'Large Counts ✓.' Vague checkmarks or symbolic inequalities without values typically do not earn full credit.
Should I use $\hat{p}$ or $p_0$ when checking Large Counts?: For a confidence interval, use the sample proportion $\hat{p}$ because there is no hypothesized value. For a significance test, use the null value $p_0$ , since the test operates under the assumption that $H_0$ is true. For a two-proportion test, use the pooled proportion. Mixing these up is one of the most common Unit 6 errors.
Can I just use my calculator's test function without showing the formula?: You can use calculator output for the computation, but you must still name the procedure, check conditions, report the test statistic and p-value (or interval endpoints), and write a conclusion in context. Reporting only calculator output with no supporting work risks losing method points. Naming the procedure, like 'one-proportion z-test,' is essential.
How do I answer a part that says 'use your confidence interval' to make a decision?: Do not run a separate significance test. Instead, check whether the null value (or 0 for a difference of proportions) falls inside the interval. If the null value is not in the interval, that is evidence against it at the corresponding significance level; if it is inside, you lack convincing evidence of a difference. Then state your conclusion in context.

Learn this with a teacher, not a page

The Crimsora tutor teaches U6 FRQ Practice live — explaining on a whiteboard, asking you questions, and adapting to where you get stuck.

Try a live session free