# Connexions

You are here: Home » Content » Collaborative Statistics Homework Book: Custom Version modified by R. Bloom » Summary of Formulas

• Collaborative Statistics: custom version modified by R. Bloom
• Preface by S. Dean and B. Illowsky
• Author Acknowledgements
• Student Welcome Letter

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### Endorsed by (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
• College Open Textbooks

This module is included inLens: Community College Open Textbook Collaborative
By: CC Open Textbook CollaborativeAs a part of collection: "Collaborative Statistics"

"Reviewer's Comments: 'I recommend this book. Overall, the chapters are very readable and the material presented is consistent and appropriate for the course. A wide range of exercises introduces […]"

Click the "College Open Textbooks" link to see all content they endorse.

Click the tag icon to display tags associated with this content.

• JVLA Endorsed

This module is included inLens: Jesuit Virtual Learning Academy Endorsed Material
By: Jesuit Virtual Learning AcademyAs a part of collection: "Collaborative Statistics"

"This is a robust collection (textbook) approved by the College Board as a resource for the teaching of AP Statistics. "

Click the "JVLA Endorsed" link to see all content they endorse.

• WebAssign

This module is included inLens: WebAssign The Independent Online Homework and Assessment Solution
By: WebAssignAs a part of collection: "Collaborative Statistics"

"Online homework and assessment available from WebAssign."

Click the "WebAssign" link to see all content they endorse.

Click the tag icon to display tags associated with this content.

#### Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
• OrangeGrove

This module is included inLens: Florida Orange Grove Textbooks
By: Florida Orange GroveAs a part of collection: "Collaborative Statistics"

Click the "OrangeGrove" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

• Bookshare

This module is included inLens: Bookshare's Lens
By: Bookshare - A Benetech InitiativeAs a part of collection: "Collaborative Statistics"

"DAISY and BRF versions of this collection are available."

Click the "Bookshare" link to see all content affiliated with them.

• Featured Content

This module is included inLens: Connexions Featured Content
By: ConnexionsAs a part of collection: "Collaborative Statistics"

"Collaborative Statistics was written by two faculty members at De Anza College in Cupertino, California. This book is intended for introductory statistics courses being taken by students at two- […]"

Click the "Featured Content" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

#### Also in these lenses

• statistics

This module is included inLens: Statistics
By: Brylie OxleyAs a part of collection: "Collaborative Statistics"

Click the "statistics" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• Lucy Van Pelt

This module is included inLens: Lucy's Lens
By: Tahiya MaromeAs a part of collection: "Collaborative Statistics"

"Part of the Books featured on Community College Open Textbook Project"

Click the "Lucy Van Pelt" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• Educational Technology Lens

This module is included inLens: Educational Technology
By: Steve WilhiteAs a part of collection: "Collaborative Statistics"

Click the "Educational Technology Lens" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• Statistics

This module is included inLens: Mathieu Plourde's Lens
By: Mathieu PlourdeAs a part of collection: "Collaborative Statistics"

Click the "Statistics" link to see all content selected in this lens.

• statf12

This module is included inLens: Statistics Fall 2012
By: Alex KolesnikAs a part of collection: "Collaborative Statistics"

Click the "statf12" link to see all content selected in this lens.

• UTEP

This module is included inLens: Amy Wagler's Lens
By: Amy WaglerAs a part of collection: "Collaborative Statistics"

Click the "UTEP" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• Make Textbooks Affordable

This module is included inLens: Make Textbooks Affordable
By: Nicole AllenAs a part of collection: "Collaborative Statistics"

Click the "Make Textbooks Affordable" link to see all content selected in this lens.

• BUS204 Homework

This module is included inLens: Saylor BUS 204 Homework
By: David BourgeoisAs a part of collection: "Collaborative Statistics"

"Homework for Discrete Variables/Probability. "

Click the "BUS204 Homework" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

• crowe

This module is included in aLens by: Chris RoweAs a part of collection: "Collaborative Statistics"

Click the "crowe" link to see all content selected in this lens.

• Bio 502 at CSUDH

This module is included inLens: Bio 502
By: Terrence McGlynnAs a part of collection: "Collaborative Statistics"

"This is the course textbook for Biology 502 at CSU Dominguez Hills"

Click the "Bio 502 at CSUDH" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Inside Collection (Textbook):

Textbook by: Roberta Bloom. E-mail the author

# Summary of Formulas

Summary: This module provides a summary on formulas used in Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

## The Chi-Square Probability Distribution

μ=dfμ=df and σ=2dfσ=2df

## Goodness-of-Fit Hypothesis Test

• Use goodness-of-fit to test whether a data set fits a particular probability distribution.
• The degrees of freedom are number of cells or categories - 1number of cells or categories - 1.
• The test statistic is Σ k ( O E ) 2 E Σ k ( O E ) 2 E , where OO = observed values (data), EE = expected values (from theory), and kk = the number of different data cells or categories.
• The test is right-tailed.

## Test of Independence

• Use the test of independence to test whether two factors are independent or not.
• The degrees of freedom are equal to (number of columns - 1)(number of rows - 1)(number of columns - 1)(number of rows - 1).
• The test statistic is Σ ( i j ) ( O - E ) 2 E Σ ( i j ) ( O - E ) 2 E where OO = observed values, EE = expected values, ii = the number of rows in the table, and jj = the number of columns in the table.
• The test is right-tailed.
• If the null hypothesis is true, the expected number E = (row total)(column total) total surveyed E= (row total)(column total) total surveyed .

## Test of Homogeneity

• Use the test for homogeneity to decide if two populations with unknown distributions have the same distribution as each other.
• The degrees of freedom are equal to number of columns - 1number of columns - 1.
• The test statistic is Σ ( i j ) ( O - E ) 2 E Σ ( i j ) ( O - E ) 2 E where OO = observed values, EE = expected values, ii = the number of rows in the table, and jj = the number of columns in the table.
• The test is right-tailed.
• If the null hypothesis is true, the expected number E = (row total)(column total) total surveyed E= (row total)(column total) total surveyed .

## Note:

The expected value for each cell needs to be at least 5 in order to use the Goodness-of-Fit, Independence and Homogeneity tests.

## Test of a Single Variance

• Use the test to determine variation.
• The degrees of freedom are the number of samples - 1.
• The test statistic is ( n - 1 ) s 2 σ 2 ( n - 1 ) s 2 σ 2 , where nn = the total number of data, s2s2 = sample variance, and σ2σ2 = population variance.
• The test may be left, right, or two-tailed.

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

#### Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

#### Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks