AP Statistics FRQ practice

Write AP Statistics free-response answers in an exam-style editor, or browse the questions by type: Question 2 FRQ and Question 4 FRQ.

📊AP Statistics

Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

FRQ	Focus	Units	Why
FRQ 1	Multi-Focus on Practices 1 and 2	1	Tests formulating an investigative question and collecting data (sampling, experimental design)
FRQ 2	Multi-Focus on Practices 3 and 4	1, 2, 5	Tests analyzing data and interpreting results — graphs, summary statistics, probability, regression output
FRQ 3	Inference	3, 4	One complete inference procedure — a hypothesis test or confidence interval for proportions or means
FRQ 4	Multi-Focus on Practices 2, 3, and 4	All	Combines content areas across the course, assessing collecting, analyzing, and interpreting together

This mapping reflects College Board's exam structure - each FRQ type tests specific skills that are taught in particular units.

Practice FRQ 11 of 1211/12

3. A team of wildlife biologists is studying the effect of a recent habitat restoration project on the growth of the marsh bellflower, a native plant species. The biologists want to determine if the true mean height of mature marsh bellflowers in the restored wetland area is greater than the true mean height of mature marsh bellflowers in an adjacent unrestored wetland area. They selected a random sample of 35 mature plants from the restored area and an independent random sample of 40 mature plants from the unrestored area. The summary statistics for the heights, in centimeters, of the plants in the two samples are shown in Table 1.

Summary Statistics for Marsh Bellflower Heights

Wetland Area	Sample Size ( $n$ )	Sample Mean ( $\bar{x}$ )	Sample Standard Deviation ( $s$ )
Restored	35	64.2	8.5
Unrestored	40	59.8	9.2

State the null and alternative hypotheses the biologists should use to test their research question. Define any parameters used.

Identify the appropriate inference procedure and verify that the conditions for this procedure are met.

Calculate the test statistic and the $p$ -value for the test.

Based on the $p$ -value calculated in Part C, what conclusion should the biologists make at the $\alpha = 0.05$ significance level? Provide your conclusion in the context of the study.