This is personal study note Copyright and original reference: https://www.youtube.com/watch?v=iraPUcOH5uw&list=PLsri7w6p16vulKaxOlNQFSWuyDuE9oEVP&index=2 ================================================================================ Estimate "population's mean parameter in interval" 1. When you know "std parameter of population" (rare case) ================================================================================ Example ================================================================================ A_company Estimate "mean lifespan of bulb" of population set Extract 200 number of bulbs sample_mean_lifespan=30000 hours population_std=500 hours Estimate "mean parameters interval" with 95% confidence (z=1.96) ================================================================================ Calculation ================================================================================ Standard deviation vs standard error $$$ \text{std} = \sqrt{\text{variance}}$$$ standard error: $$$\dfrac{\text{std from sample}}{\sqrt{n}}$$$ ================================================================================ Estimate population's mean parameter in interval 2. When you don't know std parameter of population (general case) Use sample data's std Since you don't know population's std, confidence interval becomes large And you use t distribution (when you don't know population's parameters) than z distribution ================================================================================ Example student heights 12 number students' height values with 95% confidence, estimate population's mean parameter in interval ================================================================================ Calculation Sample mean and sample std std error degree of freedom = 12-1 =11 Estimate