{"id":"study2-p-value-coin-three-bullets","audience":"college","category":"explaining","technique":"audience","track":"study","level":"intermediate","title":"Explain a p-value to a high schooler in three bullets","free":false,"task":"Your sister is a high school junior and asked what a p-value means. Get exactly 3 bullets starting with the labels Idea:, Example: and Careful:, each under 20 words, plain text. Use the coin example from your notes, and make Careful: say what a p-value is NOT, as your professor does.","materialLabel":"Your notes (attached to your prompt automatically)","material":"STAT 200 - Lecture 9 - p-values\n\nDefinition from lecture: the p-value is the probability of getting results at least as extreme as ours, ASSUMING the null hypothesis is true.\n\nCoin example: null hypothesis = the coin is fair. We flip it 10 times and get 9 heads. If the coin really is fair, the chance of 9 or more heads is about 1% (0.011). That small number makes \"fair coin\" hard to believe.\n\nSmall p-value (below 0.05 in this class) = evidence against the null.\n\nI wrote: \"p-value = the probability the null is true.\"\n** Prof. Chen: \"NO. This is the most common mistake. The p-value says nothing directly about the probability that the null is true.\" **\n\nAlso: p = 0.04 does not mean the effect is large or important.","rules":[{"type":"maxBullets","max":3},{"type":"maxWords","max":70},{"type":"plainText"}],"mistakes":[{"title":"Using your own wrong note","why":"Your notes still say the p-value is the probability the null is true.","fix":"Add: \"It is NOT the probability the null is true, per Prof. Chen.\"","checks":["r1"]},{"title":"Too much explaining","why":"The AI writes a full lecture with a heading and a summary.","fix":"Say: \"At most 3 bullets, each under 20 words.\"","checks":["r0"]},{"title":"No example","why":"Without the coin, it gets abstract fast.","fix":"Add: \"Use the coin example: 9 heads in 10 flips, about 1%.\"","checks":["r2"]},{"title":"Too many bullets","why":"The AI loves long bullet lists.","fix":"Say: \"At most 3 bullets.\"","checks":["maxBullets"]},{"title":"Trusting the AI to count words","why":"AI is bad at counting. Ask for a total and it often lands 20% over.","fix":"Cap each part: \"each line under 12 words.\"","checks":["maxWords"]},{"title":"Forgetting where it's going","why":"AI formats for a screen, with bold and headings that show up as stray symbols.","fix":"Say: \"Plain text, no bold, no headings.\"","checks":["plainText"]}],"promptHints":[{"label":"Names the reader","patterns":["high school","sister","junior"]},{"label":"Sets the bullets and labels","patterns":["(at most|max|no more than|only|exactly)\\s*(3|three)\\s*bullet","idea:.{0,30}example:"]},{"label":"Uses the coin example","patterns":["coin","9 heads"]},{"label":"Says what it is NOT","patterns":["(not|isn't).{0,40}(probability|chance).{0,30}(null|true)"]},{"label":"Limits each bullet","patterns":["under \\d+","\\d+\\s*words"]}],"hint":"Explaining a tricky idea is about the audience and the trap. Name the reader, cap the bullets, use the example, and block the classic mistake.","mission":"Explain p-values to a high school junior.","musts":["Three bullets at most","Coin example","p-value is not P(null true)"],"rubricLabels":["Has exactly 3 bullets starting with Idea:, Example: and Careful:, each under 20 words","Describes the p-value as the chance of results this extreme if the null (the coin is fair) were true, and does not say it is the probability the null is true","Uses the coin example with 9 heads out of 10 and about 1%, in plain words a high school student can follow"]}