Algebra 2 Sampling, Surveys and Experiments Test Solutions and Scoring (PDF)

Algebra 2 math test solutions: Sampling, Surveys and Experiments – Maths PDF

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This sampling inference test answers for Algebra 2 covers sampling, surveys and experiments (Common Core S-IC.A.1, S-IC.A.2, S-IC.B.3, S-IC.B.4, S-IC.B.5, S-IC.B.6), with a free PDF to print.

Use this answer key and scoring guide to grade the test on sampling, surveys, and experiments (S-IC.A.1). Each solution shows the full reasoning, and the scoring note explains how many points to award for correct setup, correct work, and a correct final answer. Partial credit rewards a sound method even when a small arithmetic slip changes the result.

Algebra 2 · Common Core State Standards: S-IC.A.1, S-IC.A.2, S-IC.B.3, S-IC.B.4, S-IC.B.5, S-IC.B.6

Sampling inference test answers: worked solutions

Question 1 – Classify studies [2 pts]

(a) Experiment: treatments are assigned at random. (b) Survey: a sample is asked questions.

(a) experiment; (b) survey

Scoring: 1 point for each classification.

Question 2 – Bias [2 pts]

The students are chosen for convenience, not at random. People at the dessert bar may like food more than other students, so the sample is biased.

Convenience sample; likely to overrepresent students who like the menu

Scoring: 1 point for each problem.

Question 3 – Margin of error [3 pts]

Completed table.

\(\frac{1}{\sqrt{400}} = 0.05\). \(54\% \pm 5\%\).

49% to 59%

Scoring: 1 point for the table, 1 point for the margin of error of 400, 1 point for the interval.

Question 4 – Read a simulation [3 pts]

Samples of 0.55 or more: 3 + 2 = 5.

(a) The bars from 0.55 have counts 3 and 2: 5 samples. (b) \(\frac{5}{20} = 0.25\). (c) Proportions near 0.65 occurred in at most 2 of 20 samples, so it is somewhat unusual but possible.

(a) 5; (b) 25%; (c) fairly unusual

Scoring: 1 point for each part.

Question 5 – Design an experiment [2 pts]

Number the plants 1 to 30. Use a random number generator to select 15 numbers for the fertilizer group; the other 15 form the control group.

Random assignment of 15 and 15

Scoring: 1 point for random assignment, 1 point for equal groups with a control.

Question 6 – Compare treatments [2 pts]

Differences stay below 1.0.

None of the 100 simulated differences reached 1.0, so a difference this large almost never happens by chance.

Yes, the treatment likely had an effect

Scoring: 1 point for the comparison, 1 point for the conclusion.

Question 7 – Sample size [2 pts]

The margin is about \(\frac{1}{\sqrt{n}}\). Half the margin needs four times the sample: \(4 \cdot 250 = 1000\).

About 1,000 voters

Scoring: 1 point for the relationship, 1 point for the answer.

Question 8 – Evaluate a report [2 pts]

The respondents chose themselves (voluntary response), so the sample is biased and does not represent all people.

Not reliable: a voluntary response sample is biased

Scoring: 1 point for identifying the self-selected sample, 1 point for the conclusion.

Question 9 – Find the error [2 pts]

Students chose whether to eat breakfast, so other variables could explain the difference. Only a randomized experiment can show cause and effect.

Observational studies cannot establish cause

Scoring: 1 point for confounding, 1 point for the correct statement.

Total score

Total

20 points

Key facts behind this sampling inference test answers

Key facts

A random sample is representative; a convenience sample is biased.
Surveys, observational studies, and experiments answer different questions.
Random assignment supports cause-and-effect conclusions.
Margin of error for a proportion ≈ 1/√n.
Simulation shows how likely a result is by chance.

How to use this sampling inference 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.

Download the sampling inference test answers as a PDF with the button below and keep it with your notes.

All Algebra 2 chapters: Algebra 2 math.

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