Standard Error
The standard error (SE) is the standard deviation of a statistic's sampling distribution. For the sample mean, SE(x̄) = σ/√n. The standard error decreases with larger sample size, indicating better precision. It's the key quantity for calculating confidence intervals and p-values in hypothesis tests.
Real World
Pfizer increased its COVID-19 vaccine trial from 30,000 to 44,000 participants partly to shrink the standard error of its efficacy estimate, giving regulators more precise results.
Exam Focus
Remember SE decreases with √n, so quadrupling sample size halves the standard error — a common numerical trap.
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