Give Me 8 Minutes, I'll Make Statistics Click Forever

A coffee shop says the average wait is 3 minutes. You time 25 customers and get 3.6. Is the shop lying? One question, followed all the way through, builds the whole core of statistics: sample and population, mean and standard deviation, the sampling distribution, the standard error, the central limit theorem, z-scores, p-values, confidence intervals and the two kinds of error. Every number on screen comes from real simulation, and at the end the whole method runs in 9 lines of Python. The twist: with 25 customers, an average of 3.6 is weak evidence (p = 0.31). With 100 customers, the same 3.6 is strong evidence (p = 0.045). The average never changed; the standard error halved. Chapters 0:00 Is the shop lying? (the whole idea in 60 seconds) 1:03 Population and sample 1:33 Mean and standard deviation 2:18 Problem 1: one sample is noisy 2:55 Problem 2: the standard error 3:38 Problem 3: why averages make a bell (CLT) 4:10 The z score 4:33 The p value 5:11 Pop quiz: what a p value means 5:35 Same average, 100 customers 6:05 Confidence intervals (and what 95% means) 7:06 Two ways to be wrong 7:32 The whole method in 9 lines of Python 7:53 The board, filled in Waits are simulated as exponential (most short, a few long). Honest shop: average 3 minutes. The 25 waits come from a shop whose true average is 3.6. Next: regression, on the same board. #statistics #pvalue #confidenceinterval #hypothesistesting #datascience #GATEDA