Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Collaborative Statistics » Practice 3: Confidence Intervals for Proportions

Navigation

Table of Contents

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 collection is included inLens: Community College Open Textbook Collaborative
    By: CC Open Textbook Collaborative

    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.

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 collection is included inLens: Florida Orange Grove Textbooks
    By: Florida Orange Grove

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

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

  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    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

  • Lucy Van Pelt display tagshide tags

    This collection is included inLens: Lucy's Lens
    By: Tahiya Marome

    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 collection is included inLens: Educational Technology
    By: Steve Wilhite

    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.

  • crowe

    This collection is included in aLens by: Chris Rowe

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

  • Exercises

    This module is included inLens: Mihai Nica's Lens
    By: Mihai Nica

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

  • Bio 502 at CSUDH display tagshide tags

    This collection is included inLens: Bio 502
    By: Terrence McGlynn

    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.
 

Practice 3: Confidence Intervals for Proportions

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

Student Learning Outcomes

  • The student will calculate confidence intervals for proportions.

Given

The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 - 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 - 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class is a random sample of the population.

Estimated Distribution

Exercise 1

What is being counted?

Exercise 2

In words, define the Random Variable XX size 12{X} {}. X=X= size 12{X={}} {}

Solution

The number of girls, age 8-12, in the beginning ice skating class

Exercise 3

Calculate the following:

  • a. x=x= size 12{x={}} {}
  • b. n=n= size 12{n={}} {}
  • c. p'=p'= size 12{p'={}} {}

Solution

  • a. 64
  • b. 80
  • c. 0.8

Exercise 4

State the estimated distribution of XX size 12{X} {}. XX ~

Solution

B ( 80 , 0.80 ) B(80,0.80)

Exercise 5

Define a new Random Variable P'P' size 12{P'} {}. What is p'p' size 12{p'} {} estimating?

Solution

p p

Exercise 6

In words, define the Random Variable P'P' size 12{P'} {} . P'=P'= size 12{P'={}} {}

Solution

The proportion of girls, age 8-12, in the beginning ice skating class.

Exercise 7

State the estimated distribution of P'P' size 12{P'} {}. P'P' ~

Explaining the Confidence Interval

Construct a 92% Confidence Interval for the true proportion of girls in the age 8 - 12 beginning ice-skating classes at the Ice Chalet.

Exercise 8

How much area is in both tails (combined)? α=α= size 12{α={}} {}

Solution

1 - 0.92 = 0.08

Exercise 9

How much area is in each tail? α2=α2= size 12{ { {α} over {2} } ={}} {}

Solution

0.04

Exercise 10

Calculate the following:

  • a. lower limit =
  • b. upper limit =
  • c. error bound =

Solution

  • a. 0.72
  • b. 0.88
  • c. 0.08

Exercise 11

The 92% Confidence Interval is:

Solution

(0.72; 0.88)

Exercise 12

Figure 1
Fill in the blanks on the graph with the areas, upper and lower limits of the Confidence Interval, and the sample proportion.
Normal distribution curve with two vertical upward lines from the x-axis to the curve. The confidence interval is between these two lines. The residual areas are on either side.

Exercise 13

In one complete sentence, explain what the interval means.

Discussion Questions

Exercise 14

Using the same p'p' size 12{p'} {} and level of confidence, suppose that n were increased to 100. Would the error bound become larger or smaller? How do you know?

Exercise 15

Using the same p'p' size 12{p'} {} and n=80n=80 size 12{n="80"} {}, how would the error bound change if the confidence level were increased to 98%? Why?

Exercise 16

If you decreased the allowable error bound, why would the minimum sample size increase (keeping the same level of confidence)?

Collection Navigation

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:

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? 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

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