[Verse 1] When you sample from the crowd, just a fraction of the whole The true mean hides somewhere, that's your estimation goal Take your sample average, add and subtract the space Margin of error builds your statistical embrace [Chorus] Confidence intervals, capture what's real Ninety-five percent, that's the standard deal Lower bound, upper bound, range where truth might dwell Confidence intervals tell the story well CI equals X-bar plus or minus ME Statistical fences around uncertainty [Verse 2] Standard error measures how your estimates might roam Multiply by t-score when the population's unknown Sample size grows larger, margin shrinks down tight Confidence level rises, wider bounds take flight [Chorus] Confidence intervals, capture what's real Ninety-five percent, that's the standard deal Lower bound, upper bound, range where truth might dwell Confidence intervals tell the story well CI equals X-bar plus or minus ME Statistical fences around uncertainty [Bridge] If you built a hundred intervals the same exact way Ninety-five would trap the parameter, five would drift away Alpha level chosen determines your confidence grade Point-oh-five leaves room for error in the estimates you've made [Verse 3] Portfolio returns and economic forecasts too Risk assessment relies on intervals to guide you through T-distribution when sigma's not in sight Z-score works when population variance is right [Chorus] Confidence intervals, capture what's real Ninety-five percent, that's the standard deal Lower bound, upper bound, range where truth might dwell Confidence intervals tell the story well CI equals X-bar plus or minus ME Statistical fences around uncertainty [Outro] From your sample to the world, build your estimate with care Confidence intervals show how much precision's really there
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