Formula Review

Introductory Business Statistics 2eFormula Review

Formula Review

9.3 Probability Distribution Needed for Hypothesis Testing

Sample size	Test statistic
< 30 (σ unknown)	$t_{c} = \frac{\bar{X} - μ_{0}}{s / \sqrt{n}}$
< 30 (σ known)	$Z_{c} = \frac{\bar{X} - μ_{0}}{σ / \sqrt{n}}$
> 30 (σ unknown)	$Z_{c} = \frac{\bar{X} - μ_{0}}{s / \sqrt{n}}$
> 30 (σ known)	$Z_{c} = \frac{\bar{X} - μ_{0}}{σ / \sqrt{n}}$

Table 9.7 Test Statistics for Test of Means, Varying Sample Size, Population Known or Unknown

9.4 Full Hypothesis Test Examples

Test statistic for a hypothesis test of proportions:

$Z_{c} = \frac{p' - p_{0}}{\sqrt{\frac{p_{0} (1 - p 0)}{n}}}$

Previous Next

Order a print copy

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Attribution information

If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
Access for free at https://openstax.org/books/introductory-business-statistics-2e/pages/1-introduction
If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
Access for free at https://openstax.org/books/introductory-business-statistics-2e/pages/1-introduction

Citation information

Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Alexander Holmes, Barbara Illowsky, Susan Dean
- Publisher/website: OpenStax
- Book title: Introductory Business Statistics 2e
- Publication date: Dec 13, 2023
- Location: Houston, Texas
- Book URL: https://openstax.org/books/introductory-business-statistics-2e/pages/1-introduction
- Section URL: https://openstax.org/books/introductory-business-statistics-2e/pages/9-formula-review

© Mar 19, 2026 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.