Null and Alternative Hypotheses: What Are We Testing?

A new teaching method, a redesigned production process, or a new treatment may look promising. Hypothesis testing starts by defining a precise population question before looking for a small p-value. The null and alternative hypotheses are competing statements about that question, not statements about what we hope will happen. Learn with a fictional teaching example. Fictional randomized treatment-versus-usual-care example. Δ denotes a specified population mean improvement difference. Standard two-sided H₀:Δ=0 versus H₁:Δ≠0; directional Δ greater than 0 is preplanned only. p=.03 and p=.24 are explicitly hypothetical alternative study outputs, not derived from invented raw data. Alpha controls long-run rejection under a true null for valid procedures; it is not a posterior error probability. Covers Type I/II errors, nonrejection versus equivalence, and effect size/interval interpretation. Explore https://datastatpro.com Like, subscribe, and share. Further reading: https://openstax.org/books/introducto... CHAPTERS 00:00 What claim are we testing? 00:21 Define the treatment question 00:41 The null hypothesis 00:59 The alternative hypothesis 01:17 One-sided or two-sided? 01:38 Set the decision rule 01:57 What does the p-value ask? 02:15 Example: a small p-value 02:35 Example: a larger p-value 02:55 Two ways to make an error 03:16 The takeaway 03:37 Statistics made simple #Statistics #DataStatPro #StatisticsExplained