A rigorous statistical investigation into test completion times of 1,000 students — revealing patterns, gender dynamics, and population-level insights through four precision confidence intervals.
From a single starting point in a random number table, 60 unique students were selected. Their completion times and gender reveal a story of statistical equity and consistent human performance.
Each interval is a precisely calculated window into the population. Together they answer four distinct questions about student performance and demographics.
Each data point is encoded across four dimensions: time (X), rank (Y), gender (color), and deviation from mean (size). Click any dot to see full student details.
Complete dataset. Click column headers to sort · Search by ID · Click any row to highlight on scatter plot.
| # | Student ID | Gender | Time (min) | vs. Mean | Visual |
|---|
Four confidence intervals, one coherent story: this standardized test is well-calibrated, equitable across gender, and produces consistent results population-wide.
The 95% CI of (44.84, 49.90) min confirms students typically need 45–50 minutes — consistent with the test's design intent and a well-calibrated standardized instrument.
The male and female 90% CIs overlap almost completely — (44.76, 49.78) vs. (45.20, 49.74) minutes — providing strong statistical evidence of no gender-based performance gap.
The 99% CI for female proportion (0.317–0.650) centers at 0.48, very close to 50/50. The wide interval at 99% confidence reflects the precision trade-off.
With n=60, the CLT ensures z-interval validity without requiring normality. All Rule of Five conditions were verified. Sampling was without replacement using a certified random number table.