{"id":"study2-statistics-cram-sheet-three-sections","audience":"college","category":"studying","technique":"format","track":"study","level":"intermediate","title":"Build a test-day cram sheet with Formulas, Watch out, Skip","free":false,"task":"Make a cram sheet for tomorrow's Statistics exam in exactly three sections headed Formulas, Watch out and Skip, plain text, under 120 words, using only your professor's email. There is no formula sheet on the exam. Use the corrected z value.","materialLabel":"Your professor's review email (attached to your prompt automatically)","material":"From: Prof. Leung\nSubject: Exam 2 review\n\nExam 2 is tomorrow. No formula sheet is provided, and calculators are allowed.\n\nCovered: z-scores, confidence intervals for a mean (population standard deviation known), hypothesis test for a mean.\n\nFormulas to know cold:\nz = (x - mean) / sd\nConfidence interval = sample mean +/- z* x (sigma / sqrt(n))\nFor 95% confidence, z* = 1.69 (correction below)\n\nCORRECTION: I mistyped. For 95% confidence z* = 1.96.\n\nCommon mistakes I see every year:\n- Dividing by sigma instead of sigma / sqrt(n) in the interval.\n- Saying \"there is a 95% chance the true mean is inside this interval.\" The 95% describes the method, not one interval.\n\nNOT on this exam: t-distribution, chi-square tests, regression. Don't spend time on them.","rules":[{"type":"maxWords","max":120},{"type":"plainText"}],"mistakes":[{"title":"Using the typo","why":"The email's first z* value is wrong and the AI copies it.","fix":"Add: \"Use z* = 1.96, per the correction.\"","checks":["r1"]},{"title":"No fixed sections","why":"Without exact headings you get one long summary.","fix":"Say: \"Three sections: Formulas, Watch out, Skip.\"","checks":["r0"]},{"title":"Skipping the Skip list","why":"The AI includes everything it knows about stats.","fix":"Add: \"Skip lists what is NOT on the exam.\"","checks":["r2"]},{"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 three sections","patterns":["formulas.{0,40}watch out.{0,40}skip"]},{"label":"Uses the professor's email","patterns":["email","leung","professor"]},{"label":"Uses the correction","patterns":["1\\.96","correct"]},{"label":"Limits the length","patterns":["\\d+\\s*words","under \\d+"]},{"label":"Says plain text","patterns":["plain text","no (bold|headings?)"]}],"hint":"A cram sheet is only useful if it is short and exact. Name the sections, use the email only, and pass along the correction.","mission":"Make a one-page cram sheet for tomorrow's exam.","musts":["Three exact sections","Use z* of 1.96","Plain text"],"rubricLabels":["Has exactly three sections headed Formulas, Watch out and Skip, in that order","Formulas includes the z-score formula and the confidence interval formula, and gives z* for 95% as 1.96 (not 1.69)","Skip lists t-distribution, chi-square tests and regression, and none of those three appear in Formulas or Watch out"]}