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📊AP Statistics
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📊AP Statistics

FRQ 5 – Multi-Focus
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Unit 6: Inference for Categorical Data: Proportions
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AP Stats FRQ Types & Units

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

FRQFocusUnitsWhy
FRQ 1Exploring Data1, 2Tests describing/analyzing data (distributions, scatterplots, correlation)
FRQ 2Sampling & Experimental Design3 onlyTests designing studies, identifying bias, randomization - all Unit 3 content
FRQ 3Probability & Sampling Distributions4, 5Tests probability calculations, expected value, sampling distributions
FRQ 4Inference6, 7, 8, 9Tests hypothesis tests and confidence intervals - each unit covers a different inference type
FRQ 5Multi-FocusAllCombines multiple skills across units in one integrated question
FRQ 6Investigative TaskAllOpen-ended investigation that can draw from any content

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

Practice FRQ 1 of 131/13

5. According to a 2015 agricultural report, the proportion of households in City Z that maintained a vegetable garden was 0.35. Dr. Aris, a researcher, believes that the proportion of households in City Z that maintain a vegetable garden is different in 2024 than it was in 2015. To investigate this belief, Dr. Aris selected a random sample of 200 households in City Z in 2024 and recorded the number of vegetable varieties grown by each household. The distribution of the number of vegetable varieties for the sampled households is summarized in the table.

Distribution of Vegetable Varieties for the 200 Sampled Households

Number of Vegetable Varieties

0

1

2

3

4

Proportion of Households

0.55

0.20

0.15

0.08

0.02

A.
i.

A household from the sample will be selected at random. What is the probability that the household grew more than 2 vegetable varieties? Show your work.

ii.

Calculate the mean number of vegetable varieties for the sample of households in 2024. Show your work.

B.
i.

Dr. Aris defines a household as maintaining a vegetable garden if they grow at least 1 vegetable variety. In the context of Dr. Aris's investigation, state the hypotheses for the test concerning the population proportion of households that maintain a vegetable garden.

ii.

Explain, in context, what a Type I error would be for Dr. Aris's hypothesis test.

C.

A colleague, Sarah, suggests using a confidence interval to investigate whether the proportion of households in City Z that maintain a vegetable garden in 2024 is different from 0.35. Assume the conditions for inference have been met. Using Dr. Aris's data, Sarah calculated a one-sample 95 percent confidence interval for the population proportion as (0.381, 0.519). Based on the confidence interval, what conclusion can be made for Dr. Aris's hypothesis test in part B at alpha = 0.05? Justify your answer.

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FRQ Directions
Free Response Question Practice

This practice environment simulates the AP AP Statistics Free Response Questions section. Here are some guidelines:

  • Read each question carefullybefore responding. Pay attention to command verbs like "identify," "explain," "analyze," or "evaluate."
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Tip: Answer all parts of each question. Partial credit is often available, so even if you are unsure, provide what you know.