LEARN · EXPLAIN · REVISE

Calculate χ² for the table.

Read the idea, work independently, then explain what changed.

TOPIC 01

Statistical analysis of paired data: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

O=\begin{pmatrix}64&32\\32&64\end{pmatrix}

Observations must be independent; expected counts support the supplied large-sample approximation. Rejection is evidence of association, not causation.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the paired-data summaries, preserving which observations belong together.

Hint 2

All expected cells are 3u/2.

Worked solution

Use the paired-data summaries, preserving which observations belong together.
Apply the stated relation and retain its conditions.
$\chi^2=4[(32/2)^2/(96/2)]=64/3$
All four nonnegative cell contributions must be included.

The requested value is 21.3333333333.

Checks and common pitfalls: All four nonnegative cell contributions must be included.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment