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University Introductory Statistics In the University Introductory Statistics bundle

University Introductory Statistics Two-Sample Inference and Chi-Square Tests — Unit Notes

Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 7 definitions and 7 theorems, 7 worked examples, 2 diagrams, in 16 printable pages. This page lists what the notes cover. The notes themselves come with the University Introductory Statistics bundle.

Unit notes — in the bundle

16 pages 14 definitions & theorems 7 worked examples 35 key words 7 Try-it pairs, answered 14-row at-a-glance table 35-entry glossary Fill-in-the-blank guided twin 2 diagrams Letter size, print-ready

Not sold separately. The practice worksheet for this unit is free, with no email and no account.

Two-Sample Inference and Chi-Square Tests — what the notes cover

8 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.

What you need

Also in this section: 1 note on method and common errors.

Comparing two means from independent samples

  • Theorem — Sampling distribution of a difference of two sample means
  • Theorem — Large-sample z procedures for a difference of means

Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.

The pooled two-sample t procedure

  • Definition — Pooled estimate of a common variance
  • Theorem — Pooled two-sample t procedures

Also in this section: 1 worked example, 1 note on method and common errors.

Paired data and the t procedure on differences

  • Definition — Paired data and the sample of differences
  • Theorem — Paired t procedures

Also in this section: 1 worked example, 1 note on method and common errors.

Comparing two proportions

  • Definition — Pooled sample proportion
  • Theorem — Large-sample z procedures for a difference of proportions

Also in this section: 1 worked example, 1 note on method and common errors.

The chi-square goodness-of-fit test

  • Definition — Expected counts under a stated model
  • Theorem — Chi-square goodness-of-fit test

Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.

Two-way tables and the test of independence

  • Definition — Expected counts in a two-way table
  • Theorem — Chi-square test of independence

Also in this section: 1 worked example, 1 note on method and common errors.

Association and causation in categorical data

  • Definition — Conditional distributions of a two-way table
  • Definition — What a rejection of independence licenses

Also in this section: 1 worked example, 1 note on method and common errors.

Where the notes are

The notes are one of the documents in the University Introductory Statistics Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Two-Sample Inference and Chi-Square Tests practice worksheet is free and stays free.

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Practise it, then test yourself

Notes on their own do not make anything stick. This unit has a free, printable practice worksheet.

Two-Sample Inference and Chi-Square Tests practice worksheet  

← All 9 University Introductory Statistics unit notes

Free practice worksheet

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