Problem preview
S-IC.4 Warmup M3-050-A07-V01

Use sample data to estimate population means/proportions and develop margins of error using simulation.

Compare how the margin of error changes when sample size or variability changes

Problem

How does the \(\text{margin}~\text{of}~\text{error}\) change in this situation: \(n=100\) vs \(n=1000\) from same population?

Big Picture

What this problem is really about

Hold the population and confidence method fixed, then identify which factor changes. A larger random sample reduces the typical sample-to-sample variation of an estimate, so its standard error and margin of error shrink, roughly with one over the square root of sample size in common settings. Greater underlying variability would push uncertainty in the opposite direction.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
S-IC.4
Category
Statistics and Probability
Domain
Making Inferences and Justifying Conclusions
Objective
Use sample data to estimate population means/proportions and develop margins of error using simulation.
Problem type
Compare how the margin of error changes when sample size or variability changes