Explain a concept with a worked example and where it stops working

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Task: Definition-to-confusion map with source locations. Here is my course's definition of p-value, and here is my question: is the p-value the probability that the null hypothesis is true? Restate the definition exactly as my source gives it, point to where in the source each part comes from, and explain precisely where my question diverges from the definition. Mark anything the source does not settle. Task: Source-aligned explanation with a worked example, counterexample and self-check. Using the confirmed map, write a short explanation that answers my question, then: a worked example that computes a p-value for a simple two-sided test, a counterexample showing a case where the tempting interpretation fails, and three self-check questions that follow from my course source. Keep the source's exact terminology and mark anything that goes beyond it.

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Task: Definition-to-confusion map whose rows cite the exact source passages. Using only the sources in this notebook, quote my course's definition of p-value exactly, cite the passage, and explain where my question - is the p-value the probability the null hypothesis is true - diverges from that definition. Cite every claim to a passage and mark what the source does not settle. Task: Source-aligned explanation with a worked example, counterexample and self-check. Draft the explanation answering my question, keeping citations to the source for every definitional claim. Then add a worked example computing a p-value for a simple two-sided test, a clearly marked counterexample showing where the tempting interpretation fails, and three self-check questions that follow from the source. Mark everything that goes beyond the source.

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Task: Draft a study package from the source I paste. Quote the course definition once, exactly, then write: a plain restatement, one worked example, one counterexample that shows where the idea stops working, and a short self-check. Use only the pasted source for claims; if something is not in the source, say so instead of inventing it. Source: [paste the source passage]. My question: [paste your question].

What to paste into the tool

Task: Make my checked study package clearer without changing any claim. Keep the quoted course definition exactly as it is. If a clearer wording would change the meaning of a line, flag that line instead of rewriting it. My checked package: [paste it].