# Hypotheses, critical region, and p-value

> ML Prep screening item.

- Stable ID: `math-stats-07-one-sided-z-test`
- Collection: screening
- Area: Mathematics
- Topic: Statistics
- Origin: original
- Difficulty: medium
- Expected time: 4 minutes
- Skills: null-alternative, p-values, critical-regions
- Item JSON: https://mlprep.iwase.dev/item/math-stats-07-one-sided-z-test.json

## Problem

For a normal population with known standard deviation $5$, a sample of size $25$ has
mean $2$. Test $H_0:\mu=0$ against $H_1:\mu>0$ at $\alpha=0.05$. Give the $z$ statistic,
p-value, critical region in terms of $\bar X$, and decision. Use $z_{0.95}=1.645$.


## Answer policy

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## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `math-stats-07-one-sided-z-test`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.