# One-sided test, critical value, and p-value

> ML preparation item.

- Stable ID: `mit-18-05-s2022-exam2-ii4`
- Area: Mathematics
- Topic: Statistics
- Origin: external
- Expected time: 12 minutes
- Skills: hypothesis-testing, critical-value, p-value, decision-rule
- Item JSON: https://mlprep.iwase.dev/data/items/mit-18-05-s2022-exam2-ii4.json

This site does not reproduce the third-party problem.

- Source: MIT 18.05 Introduction to Probability and Statistics
- Document: Exam 2
- Locator: Question II.4, page 9
- Original problem: https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2022/resources/mit18_05_s22_exam02_pdf/
- Official answer: https://ocw.mit.edu/courses/18-05-introduction-to-probability-and-statistics-spring-2022/resources/mit18_05_s22_exam02_sol_pdf/
- Answer status: official-solution


## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `mit-18-05-s2022-exam2-ii4`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.