{
  "schema": "ml-prep/item@1",
  "item": {
    "id": "mit-18-05-s2022-pset11-q1",
    "area": "mathematics",
    "topic": "statistics",
    "origin": "external",
    "title": "Confidence intervals with known and unknown variance",
    "skills": [
      "confidence-intervals",
      "standard-error",
      "sampling-distributions"
    ],
    "priority": "core",
    "difficulty": "easy",
    "estimated_minutes": 14,
    "prerequisites": [
      "gaussian-distribution"
    ],
    "source_id": "mit-18-05-s2022",
    "locator": {
      "document": "Problem Set 11",
      "label": "Problem 1(a–c)",
      "page": 1,
      "solution_pages": "1"
    },
    "links": {
      "problem": "https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2022/resources/mit18_05_s22_pset11_pdf/",
      "solution": "https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2022/resources/mit18_05_s22_pset11_sol_pdf/"
    },
    "selection_note": "Contrasts t and z intervals on the same data and extends the calculation to sample-size planning.",
    "answer_status": "official-solution"
  }
}