Skip to ContentGo to accessibility pageKeyboard shortcuts menu
Statistics

# Chapter Review

StatisticsChapter Review

Menu

### 10.1Two Population Means with Unknown Standard Deviations

Two population means from independent samples where the population standard deviations are not known

• Random variable: $X ¯ 1 − X ¯ 2 X ¯ 1 − X ¯ 2$ = the difference of the sampling means
• Distribution: Student’s t-distribution with degrees of freedom (variances not pooled)

### 10.2Two Population Means with Known Standard Deviations

A hypothesis test of two population means from independent samples where the population standard deviations are known (typically approximated with the sample standard deviations) will have these characteristics:

• Random variable: $X ¯ 1 − X ¯ 2 X ¯ 1 − X ¯ 2$ = the difference of the means
• Distribution: normal distribution

### 10.3Comparing Two Independent Population Proportions

Test of two population proportions from independent samples

• Random variable: $p ^ A – p ^ B = p ^ A – p ^ B =$ difference between the two estimated proportions
• Distribution: normal distribution

### 10.4Matched or Paired Samples (Optional)

A hypothesis test for matched or paired samples (t-test) has these characteristics:

• Test the differences by subtracting one measurement from the other measurement
• Random variable: $x ¯ d x ¯ d$ = mean of the differences.
• Distribution: Student’s t distribution with n – 1 degrees of freedom.
• If the number of differences is small (less than 30), the differences must follow a normal distribution.
• Two samples are drawn from the same set of objects.
• Samples are dependent.
Order a print copy

As an Amazon Associate we earn from qualifying purchases.

Citation/Attribution

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

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/statistics/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/statistics/pages/1-introduction
Citation information

© Jun 7, 2022 Texas Education Agency (TEA). 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.