Skip to content Skip to navigation

OpenStax_CNX

You are here: Home » Content » F Distribution and One-Way ANOVA: Review

Navigation

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? tag icon

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

This content is ...

Endorsed by Endorsed (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 display tagshide tags

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

    Comments:

    "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 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"

    Comments:

    "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 display tagshide tags

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

    Comments:

    "Online homework and assessment available from WebAssign."

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

    Click the tag icon 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 display tagshide tags

    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 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"

    Comments:

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

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

  • Featured Content display tagshide tags

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

    Comments:

    "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 tag icon to display tags associated with this content.

Also in these lenses

  • statistics display tagshide tags

    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 tag icon to display tags associated with this content.

  • Lucy Van Pelt display tagshide tags

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

    Comments:

    "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 tag icon to display tags associated with this content.

  • Educational Technology Lens display tagshide tags

    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 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 display tagshide tags

    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 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 display tagshide tags

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

    Comments:

    "Homework for Discrete Variables/Probability. "

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

    Click the tag icon 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 display tagshide tags

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

    Comments:

    "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 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.
 

F Distribution and One-Way ANOVA: Review

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

Summary: This module provides a review of F Distribution and One-Way ANOVA as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

The next two questions refer to the following situation:

Suppose that the probability of a drought in any independent year is 20%. Out of those years in which a drought occurs, the probability of water rationing is 10%. However, in any year, the probability of water rationing is 5%.

Exercise 1

What is the probability of both a drought and water rationing occurring?

Solution

0.02

Exercise 2

Out of the years with water rationing, find the probability that there is a drought.

Solution

0.40

The next three questions refer to the following survey:

Table 1: Favorite Type of Pie by Gender
  apple pumpkin pecan
female 40 10 30
male 20 30 10

Exercise 3

Suppose that one individual is randomly chosen. Find the probability that the person’s favorite pie is apple or the person is male.

Solution

100 140 100 140 size 12{ { { size 8{"100"} } over { size 8{"140"} } } } {}

Exercise 4

Suppose that one male is randomly chosen. Find the probability his favorite pie is pecan.

Solution

10 60 10 60 size 12{ { { size 8{"10"} } over { size 8{"60"} } } } {}

Exercise 5

Conduct a hypothesis test to determine if favorite pie type and gender are independent.

Solution

p-value=0p-value=0; Reject null; Conclude dependent events

The next two questions refer to the following situation:

Let’s say that the probability that an adult watches the news at least once per week is 0.60.

Exercise 6

We randomly survey 14 people. On average, how many people do we expect to watch the news at least once per week?

Solution

8.4

Exercise 7

We randomly survey 14 people. Of interest is the number that watch the news at least once per week. State the distribution of XX. XX ~

Solution

B 14 , 0 . 60 B 14 , 0 . 60 size 12{B left ("14",0 "." "60" right )} {}

Exercise 8

The following histogram is most likely to be a result of sampling from which distribution?

Figure 1
Histogram with 7 bars.

  • A. Chi-Square
  • B. Geometric
  • C. Uniform
  • D. Binomial

Solution

D

Exercise 9

The ages of De Anza evening students is known to be normally distributed with a population mean of 40 and a population standard deviation of 6. A sample of 6 De Anza evening students reported their ages (in years) as: 28; 35; 47; 45; 30; 50. Find the probability that the mean of 6 ages of randomly chosen students is less than 35 years. Hint: Find the sample mean.

Solution

0.3669

The next three questions refer to the following situation:

The amount of money a customer spends in one trip to the supermarket is known to have an exponential distribution. Suppose the mean amount of money a customer spends in one trip to the supermarket is $72.

Exercise 10

Find the probability that one customer spends less than $72 in one trip to the supermarket?

Solution

0.6321

Exercise 11

Suppose 5 customers pool their money. (They are poor college students.) How much money altogether would you expect the 5 customers to spend in one trip to the supermarket (in dollars)?

Solution

$360

Exercise 12

State the distribution to use if you want to find the probability that the mean amount spent by 5 customers in one trip to the supermarket is less than $60.

Solution

N 72 , 72 5 N 72 , 72 5 size 12{N left ("72", { { size 8{"72"} } over { size 8{ sqrt {5} } } } right )} {}

Exercise 13

A math exam was given to all the fifth grade children attending Country School. Two random samples of scores were taken. The null hypothesis is that the mean math scores for boys and girls in fifth grade are the same. Conduct a hypothesis test.

Table 2
  n n size 12{n} {} x ¯ x ¯ size 12{ {overline {x}} } {} s 2 s 2 size 12{s rSup { size 8{2} } } {}
Boys 55 82 29
Girls 60 86 46

Solution

p-value=0.0006p-value=0.0006; Reject null; Conclude averages are not equal

Exercise 14

In a survey of 80 males, 55 had played an organized sport growing up. Of the 70 females surveyed, 25 had played an organized sport growing up. We are interested in whether the proportion for males is higher than the proportion for females. Conduct a hypothesis test.

Solution

p-value=0p-value=0; Reject null; Conclude proportion of males is higher

Exercise 15

Which of the following is preferable when designing a hypothesis test?

  • A. Maximize αα size 12{α} {} and minimize ββ size 12{β} {}
  • B. Minimize αα size 12{α} {} and maximize ββ size 12{β} {}
  • C. Maximize αα size 12{α} {} and ββ size 12{β} {}
  • D. Minimize αα size 12{α} {} and ββ size 12{β} {}

Solution

D

The next three questions refer to the following situation:

120 people were surveyed as to their favorite beverage (non-alcoholic). The results are below.

Table 3: Preferred Beverage by Age
  0 – 9 10 – 19 20 – 29 30 +   Totals
Milk 14 10 6 0 30
Soda 3 8 26 15 52
Juice 7 12 12 7 38
Totals 24 30 44 22 120

Exercise 16

Are the events of milk and 30+:

  • a. Independent events? Justify your answer.
  • b. Mutually exclusive events? Justify your answer.

Solution

  • a. No
  • b. Yes, P Mand 30 + = 0 P Mand 30 + = 0 size 12{P left ( ital "Mand""30"+{} right )=0} {}

Exercise 17

Suppose that one person is randomly chosen. Find the probability that person is 10 – 19 given that he/she prefers juice.

Solution

12 38 12 38 size 12{ { { size 8{"12"} } over { size 8{"38"} } } } {}

Exercise 18

Are Preferred Beverage and Age independent events? Conduct a hypothesis test.

Solution

No; p-value=0p-value=0

Exercise 19

Given the following histogram, which distribution is the data most likely to come from?

Figure 2
Histogram with 8 bars.

  • A. uniform
  • B. exponential
  • C. normal
  • D. chi-square

Solution

A

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

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

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add 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? tag icon

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