Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Collaborative Statistics » Practice 1: Confidence Intervals for Means, Known Population Standard Deviation

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.

  • JVLA Endorsed

    This collection is included inLens: Jesuit Virtual Learning Academy Endorsed Material
    By: Jesuit Virtual Learning Academy

    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 collection is included inLens: WebAssign The Independent Online Homework and Assessment Solution
    By: WebAssign

    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 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.

  • Bookshare

    This collection is included inLens: Bookshare's Lens
    By: Bookshare - A Benetech Initiative

    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 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

  • statistics display tagshide tags

    This collection is included inLens: Statistics
    By: Brylie Oxley

    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 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.

  • Statistics

    This collection is included inLens: Mathieu Plourde's Lens
    By: Mathieu Plourde

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

  • statf12

    This collection is included inLens: Statistics Fall 2012
    By: Alex Kolesnik

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

  • UTEP display tagshide tags

    This collection is included inLens: Amy Wagler's Lens
    By: Amy Wagler

    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 collection is included inLens: Make Textbooks Affordable
    By: Nicole Allen

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

  • BUS204 Homework display tagshide tags

    This collection is included inLens: Saylor BUS 204 Homework
    By: David Bourgeois

    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.

  • 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.

  • crowe

    This collection is included in aLens by: Chris Rowe

    Click the "crowe" 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 1: Confidence Intervals for Means, Known Population Standard Deviation

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

Student Learning Outcomes

  • The student will calculate confidence intervals for means when the population standard deviation is known.

Given

The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. (http://research.fhda.edu/factbook/FH_Demo_Trends/FoothillDemographicTrends.htm

Let X=X= size 12{X={}} {} the age of a Winter Foothill College student

Calculating the Confidence Interval

Exercise 1

x¯=x¯= size 12{ {overline {x}} ={}} {}

Solution

30.4

Exercise 2

Exercise 3

15=(insert symbol here)

Solution

σσ

Exercise 4

Define the Random Variable, X¯ X , in words.

X¯ X =

Solution

the mean age of 25 randomly selected Winter Foothill students

Exercise 5

What is x¯x¯ size 12{ {overline {x}} } {} estimating?

Solution

μμ size 12{μ} {}

Exercise 6

Is σxσx size 12{σ rSub { size 8{x} } } {} known?

Solution

yes

Exercise 7

As a result of your answer to (4), state the exact distribution to use when calculating the Confidence Interval.

Solution

Normal

Explaining the Confidence Interval

Construct a 95% Confidence Interval for the true mean age of Winter Foothill College students.

Exercise 8

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

Solution

0.05

Exercise 9

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

Solution

0.025

Exercise 10

Identify the following specifications:

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

Solution

  • a. 24.52
  • b. 36.28
  • c. 5.88

Exercise 11

The 95% Confidence Interval is:__________________

Solution

(24.52,36.28)(24.52,36.28) size 12{ \( "24","52","36" "." "28" \) } {}

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 mean.
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 mean, standard deviation and level of confidence, suppose that nn size 12{n} {} were 69 instead of 25. Would the error bound become larger or smaller? How do you know?

Exercise 15

Using the same mean, standard deviation and sample size, how would the error bound change if the confidence level were reduced to 90%? Why?

Collection Navigation

Content actions

Download:

Collection 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 ...

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