A random sample of 748 voters in a large city was asked how they voted in the presidential election of 2012. Calculate chi square and the column percentages for each table below and write a brief report describing the significance of the relationships as well as the patterns you observe.
a. Presidential preference and gender
Gender  
Preference  Male  Female  Totals 
Romney  165  173  338 
Obama Totals 



b. Presidential preference and race/ethnicity
Preference  Race/Ethnicity  
White  Black  Latino  Totals  
Romney  289  5  44  338  
Obama Totals 





c. Presidential preference by education
Preference  Education  
Less than HS  HS Graduate  College Graduate  PostGraduate Degree  Totals  
Romney  30  180  118  10  338 
Obama Totals 





d. Presidential preference by religion
Preference  Religion  
Protestant  Catholic  Jewish  None  Other  Totals  
Romney  165  110  10  28  25  338 
Obama Totals 






(a)
To find:
The chi square value for the given information and test for its significance.
Given:
The given statement is,
A random sample of 748 voters in a large city was asked how they voted in the presidential election of 2012.
The given table of information is,
Preference  Gender  
Male  Female  Totals  
Romney  165  173  338 
Obama  200  210  410 
Totals  365  383  748 
Approach:
The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.
The five step model for hypothesis testing is,
Step 1. Making assumptions and meeting test requirements.
Step 2. Stating the null hypothesis.
Step 3. Selecting the sampling distribution and establishing the critical region.
Step 4. Computing test statistics.
Step 5. Making a decision and interpreting the results of the test.
Formula used:
For a chi square, the expected frequency
Where N is the total of frequencies.
The chi square statistic is given by,
Where
And
The degrees of freedom for the bivariate table is given as,
Where r is the number of rows and c is the number of columns.
Calculation:
From the given information,
The observed frequency is given as,
Substitute 338 for row marginal, 365 for column marginal and 748 for N in equation
Substitute 338 for row marginal, 383 for column marginal and 748 for N in equation
Substitute 410 for row marginal, 365 for column marginal and 748 for N in equation
Substitute 410 for row marginal, 383 for column marginal and 748 for N in equation
Consider the following table,
165  164.93  0.07  0.0049  0.00  
173  173.07  0.0049  0.00  
200  200.07  0.0049  0.00  
210  209.93  0.07  0.0049  0.00  
Total  748  748  0 
(b)
To find:
The chi square value for the given information and test for its significance.
(c)
To find:
The chi square value for the given information and test for its significance.
(d)
To find:
The chi square value for the given information and test for its significance.
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Multivariable Calculus
Calculus: Early Transcendental Functions
Finite Mathematics and Applied Calculus (MindTap Course List)
Calculus: Early Transcendentals
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: An Applied Approach (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Statistics for The Behavioral Sciences (MindTap Course List)
Calculus (MindTap Course List)
Probability and Statistics for Engineering and the Sciences
Understanding Basic Statistics
Single Variable Calculus
Intermediate Algebra
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Trigonometry (MindTap Course List)
Mathematical Applications for the Management, Life, and Social Sciences
Mathematical Excursions (MindTap Course List)
Contemporary Mathematics for Business & Consumers
Elements Of Modern Algebra
Elementary Geometry For College Students, 7e
Elementary Technical Mathematics
Calculus: Early Transcendental Functions (MindTap Course List)
Single Variable Calculus: Early Transcendentals
Calculus of a Single Variable
Finite Mathematics for the Managerial, Life, and Social Sciences
Introduction To Statistics And Data Analysis
Study Guide for Stewart's Multivariable Calculus, 8th
Elementary Geometry for College Students
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Research Methods for the Behavioral Sciences (MindTap Course List)
Statistics for Business & Economics, Revised (MindTap Course List)
STATISTICS F/BUSINESS+ECONOMICSTEXT
Research Methods for the Behavioral Sciences (MindTap Course List)
College Algebra (MindTap Course List)
Multivariable Calculus
Mathematics For Machine Technology
Calculus (MindTap Course List)
Essentials Of Statistics For Business & Economics
Discrete Mathematics With Applications
Mathematics: A Practical Odyssey
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Introductory Statistics
College Algebra
Calculus Volume 1
A First Course in Differential Equations with Modeling Applications (MindTap Course List)