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# About: Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

 Name: Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations ID: m17042 Language: English (en) Summary: This module provides an overview of hypothesis testing in situations where there are both two independent population means and known population standard deviations in statistics. Subject: Mathematics and Statistics Keywords: elementary, statistics License: Creative Commons Attribution License CC-BY 3.0 Authors: Copyright Holders: Maintainers: Latest version: 1.10 (history) First publication date: Jun 17, 2008 4:27 pm +0000 Last revision to module: Jun 14, 2012 8:35 pm +0000

 PDF: m17042_1.10.pdf PDF file, for viewing content offline and printing. Learn more. XML: m17042_1.10.cnxml XML that defines the structure and contents of the module, minus any included media files. Can be reimported in the editing interface. Learn more.

## Version History

 Version: 1.10 Jun 14, 2012 8:35 pm +0000 by Changes: `Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations: Added " mean time wax 1 lasts is longer (wax 1 is more effective) than the mean time wax 2 lasts" to the conclusion of example. Added condition that populations are normal.` Version: 1.9 Jun 11, 2012 7:40 am +0000 by Changes: `Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations: Updated graph. Changed "average" to "mean" where needed.` Version: 1.8 Feb 4, 2009 5:42 pm +0000 by Changes: `Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations: Took out the phrase "because usually you have two setts of data."` Version: 1.7 Oct 27, 2008 5:39 pm +0000 by Changes: `roles updated` Version: 1.6 Jul 31, 2008 10:59 am +0000 by Changes: `removed draft note` Version: 1.5 Jul 9, 2008 3:16 pm +0000 by Changes: `table corrections` Version: 1.4 Jul 8, 2008 7:40 pm +0000 by Changes: `post review edits` Version: 1.3 Jul 7, 2008 4:16 pm +0000 by Changes: `post review updates` Version: 1.2 Jul 2, 2008 10:47 pm +0000 by Changes: `Added equation tags, corrected wrong subscript for u2.` Version: 1.1 Jun 26, 2008 2:53 pm +0000 by Changes: `Initial publication`

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## How to Cite and Attribute This Content

The following citation styles comply with the attribution requirements for the license (CC-BY 3.0) of this work:

### American Chemical Society (ACS) Style Guide:

Dean, S.; Illowsky, B. Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations, OpenStax-CNX Web site. http://cnx.org/content/m17042/1.10/, Jun 14, 2012.

### American Medical Assocation (AMA) Manual of Style:

Dean S, Illowsky B. Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations [OpenStax-CNX Web site]. June 14, 2012. Available at: http://cnx.org/content/m17042/1.10/.

### American Psychological Assocation (APA) Publication Manual:

Dean, S., & Illowsky, B. (2012, June 14). Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations. Retrieved from the OpenStax-CNX Web site: http://cnx.org/content/m17042/1.10/

### Chicago Manual of Style (Bibliography):

Dean, Susan, and Barbara Illowsky. "Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations." OpenStax-CNX. June 14, 2012. http://cnx.org/content/m17042/1.10/.

### Chicago Manual of Style (Note):

Susan Dean and Barbara Illowsky, "Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations," OpenStax-CNX, June 14, 2012, http://cnx.org/content/m17042/1.10/.

### Chicago Manual of Style (Reference, in Author-Date style):

Dean, S., & Illowsky, B. 2012. Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations. OpenStax-CNX, June 14, 2012. http://cnx.org/content/m17042/1.10/.

### Modern Languages Association (MLA) Style Manual:

Dean, Susan, and Barbara Illowsky. Hypothesis Testing: Two Population Means and Two Population Proportions: Comparing Two Independent Population Means with Known Population Standard Deviations. OpenStax-CNX. 14 June 2012 <http://cnx.org/content/m17042/1.10/>.