Exercise 3: Mapping Each Worked-Experiment Step to Its Topic — Possible Solution ==================================================================================== STEP 1: TREATING THE HISTORICAL BASELINE AS A SAMPLE, NOT THE TRUTH — SAMPLING & THE SAMPLING DISTRIBUTION (CHAPTER 2) ------------------------------ Recognizing that a historical observed rate is a limited sample of past traffic rather than a guaranteed future truth, carrying its own sampling error, is directly Chapter 2's own population-vs-sample distinction. STEP 2: QUANTIFYING UNCERTAINTY IN THE BASELINE — CONFIDENCE INTERVALS (CHAPTER 3) ------------------------------ Building a range of plausible values around a point estimate, using a standard error and a critical value, is precisely Chapter 3's own confidence interval technique. STEP 3: STATING FORMAL HYPOTHESES BEFORE LOOKING AT DATA — HYPOTHESIS TESTING FUNDAMENTALS (CHAPTER 4) ------------------------------ Defining H0 and H1 and fixing a significance level in advance, before examining any experimental results, is Chapter 4's own hypothesis- testing framework. STEP 4: AN A/A TEST COMPARING TWO IDENTICALLY-TREATED GROUPS — THE T-TEST & COMPARING TWO GROUPS (CHAPTER 5) ------------------------------ Comparing two groups' mean session durations using a standard deviation estimated from the sample itself (not a known population sigma) is exactly Chapter 5's own Welch's two-sample t-test material. STEP 5: A PROPERLY SAMPLE-SIZE-PLANNED CONVERSION-RATE TEST — A/B TESTING IN PRACTICE (CHAPTER 6) ------------------------------ Planning sample size in advance for a target effect and power, then running a two-proportion z-test to compare conversion rates, is Chapter 6's own A/B testing material. STEP 6: RESISTING A CORRELATIONAL SHORTCUT — CORRELATION VS. CAUSATION (CHAPTER 7) ------------------------------ Recognizing that an observed correlation between two variables could reflect reverse causation rather than the tempting causal story, and refusing to draw a causal conclusion from it, is Chapter 7's own central caution. STEP 7: FITTING A PREDICTIVE LINE AND FLAGGING EXTRAPOLATION — LINEAR REGRESSION AS STATISTICAL INFERENCE (CHAPTER 8) ------------------------------ Fitting a least-squares line, computing R-squared, making a prediction, and flagging that the prediction falls outside the observed data range is Chapter 8's own regression material. STEP 8: REFRAMING THE RESULT AS AN UPDATED BELIEF — BAYESIAN INFERENCE & UPDATING BELIEFS (CHAPTER 9) ------------------------------ Starting from a prior belief and describing how strong evidence would update that belief into a posterior, contrasted against the frequentist reject/fail-to-reject framing, is Chapter 9's own Bayesian material. WHY THIS WORKS AS AN ANSWER ------------------------------ Each step is matched to its topic by identifying the specific inferential operation actually being performed - a sampling distinction, an interval estimate, formal hypotheses, a two-group comparison with an estimated standard deviation, a planned proportion test, a causal-inference caution, a predictive line fit, and a belief update - rather than simply repeating the chapter numbers already given in the original worked experiment.