Test if a sample mean differs significantly from a known population mean using statistical analysis. Input sample data and population mean to calculate t-statistics and p-values.

Check the current state of evolutionary optimization, including generation progress, population statistics, and best solutions found during genetic algorithm processes.

Perform a z-test to determine if a sample mean significantly differs from a known population mean using population standard deviation for statistical inference.

Retrieve population statistics for US states and counties using American Community Survey data to support demographic analysis and planning.

Retrieve detailed country data including population, area, capital, region, coordinates, and 20+ statistics by providing a country name, slug, or ISO code.

Calculate confidence intervals for population means using sample data to estimate statistical uncertainty in statistical inference.