# Chi-square goodness of fit

> ML Prep screening item.

- Stable ID: `math-stats-09-chi-square-fit`
- Collection: screening
- Area: Mathematics
- Topic: Statistics
- Origin: original
- Difficulty: hard
- Expected time: 5 minutes
- Skills: goodness-of-fit, chi-square
- Item JSON: https://mlprep.iwase.dev/item/math-stats-09-chi-square-fit.json

## Problem

A die is rolled $60$ times, producing face counts $(8,9,10,11,12,10)$. Test the
null hypothesis that the die is fair using a chi-square goodness-of-fit test.
Compute the statistic and degrees of freedom, and decide at $5\%$ using critical value $11.07$.


## Answer policy

The human page contains a collapsed answer. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `math-stats-09-chi-square-fit`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.