Sampling and Claims
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalThese questions grade judgment: what can a study honestly claim? The points leak in the reach, a sample's conclusion stretched to a population that was never in the frame, in the margin, an interval read as exactness, as a bound on individuals, or one-sided, and at the end, in the verb: an observed association promoted to a cause.
These patterns aren't really about computing anything. They're about whether the conclusion stayed inside the sampled population, whether the margin of error bracketed the population value both ways, and whether causal language waited for the randomized experiment that earns it.
The work
4 ways in · any order
Lesson
Sampling and Claims
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Size every conclusion to the population sampled, read margins of error as two-sided brackets on the population value, scale sample estimates honestly, and reserve causal claims for randomized experiments. The lesson works the method and the three patterns that derail it, and it saves the trap for last: the plausible-sounding cause a study never proved.
Diagnostic
10-item topic check
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Ten items across the three patterns: generalizing beyond the sample, misreading the margin of error, and claiming causation from observation. A mix of study designs, interval reads, scaled estimates, and claim audits. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
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About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.