Race  
Received Services?  Black  White  Totals 
Yes  6  7  13 
No Totals 



a. Is there a statistically significant relationship between race and whether the person has received services from the program?
b. Compute column percentages for the table to clarify the pattern of the relationship. Which group was more likely to get services?
(a)
To find:
The chi square value for the given information and test for its significance.
Given:
The given statement is,
A local politician is concerned that a program for the homeless in her city is discriminating against blacks and other minorities.
The given table of information is,
Race  
Received Services?  Black  White  Totals 
Yes  6  7  13 
No  4  9  13 
Totals  10  16  26 
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 13 for row marginal, 10 for column marginal and 26 for N in equation
Substitute 13 for row marginal, 16 for column marginal and 26 for N in equation
Substitute 13 for row marginal, 10 for column marginal and 26 for N in equation
Substitute 13 for row marginal, 16 for column marginal and 26 for N in equation
Consider the following table,
6  5  1  1  0 
(b)
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)
Calculus: Early Transcendental Functions
Finite Mathematics and Applied Calculus (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Multivariable Calculus
Applied Calculus
Calculus: An Applied Approach (MindTap Course List)
Calculus: Early Transcendentals
Precalculus: Mathematics for Calculus (Standalone Book)
Statistics for The Behavioral Sciences (MindTap Course List)
Calculus (MindTap Course List)
Understanding Basic Statistics
Probability and Statistics for Engineering and the Sciences
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Single Variable Calculus
Intermediate Algebra
Finite Mathematics
Elements Of Modern Algebra
Elementary Geometry For College Students, 7e
Trigonometry (MindTap Course List)
Mathematical Excursions (MindTap Course List)
Elementary Technical Mathematics
Contemporary Mathematics for Business & Consumers
Mathematical Applications for the Management, Life, and Social Sciences
Finite Mathematics for the Managerial, Life, and Social Sciences
Calculus: Early Transcendental Functions (MindTap Course List)
Calculus of a Single Variable
Single Variable Calculus: Early Transcendentals
Introduction To Statistics And Data Analysis
Elementary Geometry for College Students
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Study Guide for Stewart's Multivariable Calculus, 8th
Research Methods for the Behavioral Sciences (MindTap Course List)
Research Methods for the Behavioral Sciences (MindTap Course List)
Statistics for Business & Economics, Revised (MindTap Course List)
STATISTICS F/BUSINESS+ECONOMICSTEXT
Mathematics For Machine Technology
Multivariable Calculus
College Algebra (MindTap Course List)
Calculus (MindTap Course List)
Essentials Of Statistics For Business & Economics
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Discrete Mathematics With Applications
Mathematics: A Practical Odyssey
Introductory Statistics
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
College Algebra