Skip to content Skip to navigation Skip to collection information

OpenStax-CNX

You are here: Home » Content » Collaborative Statistics » Practice 1: Hypothesis Testing for Two 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.
  • 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.

  • 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: Hypothesis Testing for Two Proportions

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

Summary: This module provides a practice of Two Population Means and Two Population Proportions as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Student Learning Outcomes

  • The student will conduct a hypothesis test of two proportions.

Given

In the recent Census, 3 percent of the U.S. population reported being two or more races. However, the percent varies tremendously from state to state. (Source: http://www.census.gov/prod/cen2010/briefs/c2010br-02.pdf) Suppose that two random surveys are conducted. In the first random survey, out of 1000 North Dakotans, only 9 people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.

Hypothesis Testing: Two Proportions

Exercise 1

Is this a test of means or proportions?

Solution

Proportions

Exercise 2

State the null and alternative hypotheses.

  • a. H0:H0: size 12{H rSub { size 8{0} } :} {}
  • b. Ha:Ha: size 12{H rSub { size 8{a} } :} {}

Solution

  • a. H 0 : PN = PND H 0 : PN = PND size 12{H rSub { size 8{O} } : rSub { size 8{ ital "PN"} } = rSub { size 8{ ital "PND"} } } {}
  • a. H a : PN > PND H a : PN > PND size 12{H rSub { size 8{a} } : rSub { size 8{ ital "PN"} } > rSub { size 8{ ital "PND"} } } {}

Exercise 3

Is this a right-tailed, left-tailed, or two-tailed test? How do you know?

Solution

right-tailed

Exercise 4

What is the Random Variable of interest for this test?

Exercise 5

In words, define the Random Variable for this test.

Exercise 6

Which distribution (Normal or student's-t) would you use for this hypothesis test?

Solution

Normal

Exercise 7

Explain why you chose the distribution you did for the above question.

Exercise 8

Calculate the test statistic.

Solution

3.50

Exercise 9

Sketch a graph of the situation. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the pp size 12{p - {}} {}value.

Figure 1
Figure 1 (9-1.png)

Exercise 10

Find the pp size 12{p - {}} {}value:

Solution

0.0002

Exercise 11

At a pre-conceived α=0.05α=0.05 size 12{α=0 "." "05"} {}, what is your:

  • a. Decision:
  • b. Reason for the decision:
  • c. Conclusion (write out in a complete sentence):

Solution

  • a. Reject the null hypothesis

Discussion Question

Exercise 12

Does it appear that the proportion of Nevadans who are two or more races is higher than the proportion of North Dakotans? Why or why not?

Collection Navigation

Content actions

Download module as:

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