Use Percentage Points in a Reported Interval

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: A supplied survey report gives estimate 50% with margin ±4 percentage points. What interval is reported? Candidate answers: (A) 4% to 50% (B) 46% to 54% (C) 46% to 58% (D) 48.00% to 52.00%.
• Independent check inputs: A supplied survey report gives estimate 51% with margin ±4 percentage points. What interval is reported? Candidate answers: (A) 4% to 51% (B) 47% to 55% (C) 47% to 59% (D) 48.96% to 53.04%.

Learn the idea

Evidence quality depends on how participants and conditions are selected. Random sampling supports population generalization, random assignment supports treatment comparisons, and uncertainty summaries do not repair biased recruitment or uncontrolled causal differences. A reported estimate with an additive margin produces endpoints by subtracting and adding the margin. Percentage points measure additive differences between percentages rather than proportional percent changes.

Here is the method on the supplied teaching case. Subtract and add four percentage points: 50−4=46, 50+4=54. A margin in percentage points is not a 4% multiplicative change.

This exercise interprets a supplied report and does not compute a confidence level or validate the survey. Preserve the reported units; multiplying by a percentage factor would answer a different uncertainty question.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: A supplied survey report gives estimate 57% with margin ±4 percentage points. What interval is reported? Candidate answers: (A) 4% to 57% (B) 53% to 61% (C) 53% to 65% (D) 54.72% to 59.28%. Show the mathematical reason, not only the selected answer. Expected result: 53% to 61%. Subtract and add four percentage points: 57−4=53, 57+4=61. A margin in percentage points is not a 4% multiplicative change.

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