Domain: Problem-Solving and Data Analysis | Skill: Inference from sample statistics and margin of error | Difficulty: Easy

Statistical Inference – Easy Strategies & Practice

Ever wondered how the SAT can ask about all teachers in a school or every employee in a company when only a small sample is surveyed? That’s exactly what Inference from sample statistics and margin of error questions test. At the Easy level, the SAT simply wants to know whether you can scale up a sample proportion to a whole-group estimate and check if the answer makes sense. Master this skill and you will collect quick points in the Problem-Solving and Data Analysis domain—no fancy statistics degree required!

Typical Question Formats

Typical Format	What It Tests	Quick Strategy
A random sample of 20 out of 200 … 30% said yes. About how many of all 200 …?	Multiplying a sample proportion by total population	Convert % to decimal, multiply, round sensibly
Table showing sample counts then asks “which is closest to the predicted total?”	Interpreting two-way tables + proportion	Find row/column total first, then scale up
“Margin of error of \(\pm 4\%\) … which values are plausible for the population?”	Adding/subtracting the margin to create an interval	Compute interval, pick any answer inside

Real SAT-Style Example

Problem

A city library has 120 active volunteers. A random sample of 15 of these volunteers shows that \(40\%\) volunteer more than 5 hours per week. Based on this survey, which of the following is the best estimate of the total number of volunteers at the library who volunteer more than 5 hours per week?

A) 18     B) 36     C) 48 ✅     D) 72

Step-by-Step Solution

1. Convert \(40\%\) to a decimal: \(0.40\).
2. Multiply by total population: \(0.40 \times 120 = 48\).
3. Check if 48 appears among the choices – it does (C).

Step-by-Step Strategy (Easy Level)

1. Identify the sample statistic. Look for a percentage or fraction from the surveyed group.
2. Convert & Clarify. Change the percent to a decimal (\(25\% \to 0.25\)). Note the total population size.
3. Scale Up. Multiply the decimal by the total population to estimate the count.
4. Sense-Check. Does the answer make logical sense (e.g., can’t exceed total population)? Pick the closest choice.

Applying the Strategy to Our Example

Step 1 — Identify: Sample statistic is \(40\%\) volunteering > 5 h/wk.

Step 2 — Convert & Clarify: \(40\% = 0.40\); total volunteers \(= 120\).

Step 3 — Scale Up: \(0.40 \times 120 = 48\).

Step 4 — Sense-Check: 48 is less than 120 and matches answer choice C. ✅

Key Takeaways

• Find the sample proportion first; everything hinges on it.
• Convert percent → decimal → multiply by total population.
• Keep an eye on reasonableness—answers can’t exceed the whole!
• Practice quick arithmetic to save precious exam seconds.
• Use mytestprep.ai to turn these easy points into automatic wins.