AP Statistics Sampling Methods and Bias in Surveys Test Solutions and Scoring (PDF)

AP Statistics math test solutions: Sampling Methods and Bias in Surveys – Maths PDF

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This sampling methods test answers for AP Statistics covers sampling methods and bias in surveys (Common Core AP STAT 3.1, AP STAT 3.2, AP STAT 3.3, HSS-IC.B.3), with a free PDF to print.

Each solution includes a scoring guide. Give credit for naming the correct method or bias and for explaining why it applies to the situation described.

AP Statistics · Common Core State Standards: AP STAT 3.1, AP STAT 3.2, AP STAT 3.3, HSS-IC.B.3

Sampling methods test answers: worked solutions

Question 1 – Population and statistic [2 pts]

Population: all 3,000 members. Sample: 150 members. Statistic: \(\hat{p}=\frac{60}{150}=0.40\).

3,000 members; 150 members; 40%.

Scoring: 1 point for population and sample, 1 point for the statistic 0.40.

Question 2 – Identify the method [3 pts]

Population in three groups.

(a) Stratified random sample: some individuals are chosen from every group.

(b) In a cluster sample, entire groups are randomly chosen and every member of a chosen group is included; the other groups are not sampled at all.

Stratified; clusters include whole groups only.

Scoring: 1 point for stratified; 2 points for a correct contrast.

Question 3 – Random digits [3 pts]

Random digits.

42 selected, 17 selected, 88 skipped (out of range), 63 skipped (out of range), 17 skipped (repeat), 05 selected, 29 selected.

Members 42, 17, 05, 29.

Scoring: 1 point for reading pairs, 1 point for skipping out-of-range and repeats, 1 point for the correct list.

Question 4 – Bias in a poll [3 pts]

(a) Voluntary response bias.

(b) Only readers with strong opinions are likely to vote, and readers of the site may differ from other residents.

Voluntary response; unrepresentative; random sample.

Scoring: 1 point per part.

Question 5 – Stratified sizes [3 pts]

Fraction: \(\frac{100}{1000}=0.10\). Office: 50. Drivers: 30. Warehouse: 20.

SRS of 50 office staff, 30 drivers, and 20 warehouse workers.

Scoring: 1 point for strata, 1 point for the fraction, 1 point for the sizes.

Question 6 – Sample size and bias [2 pts]

Taking more people with the same flawed method still favors the same kinds of people.

No. A larger sample reduces variability, not bias.

Scoring: 1 point for no, 1 point for the explanation.

Question 7 – Sampling variability [2 pts]

Different students are in each sample.

Sampling variability: random samples give different statistics, but both estimate the same parameter.

Scoring: 1 point for different samples, 1 point for sampling variability.

Question 8 – Choose and justify [2 pts]

Neighborhoods differ from each other, so each should be represented.

A stratified sample (an SRS from each neighborhood) represents every neighborhood.

Scoring: 1 point for stratified, 1 point for the reason.

Total score

Total

20 points

Key facts behind this sampling methods test answers

Key facts

Population vs sample; parameter vs statistic.
SRS gives every group of n individuals an equal chance; stratified takes an SRS from every stratum; cluster surveys all members of randomly chosen clusters.
Convenience and voluntary response samples are biased.
Sources of bias: undercoverage, nonresponse, response bias, voluntary response.
A larger random sample reduces sampling variability but never fixes bias.

How to use this sampling methods test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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