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





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





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






10.15
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 column percentages, strength and pattern of relationship.
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  Race/Ethnicity  
White  Black  Latino  Totals  
Romney  289  5  44  338 
Obama  249  95  66  410 
Totals  538  100  110  748 
Approach:
If the Cramer’s V value is less than 0.10, it is said that there is a weak association between the categories.
If the Cramer’s V value lies between 0.11 and 0.30, it is said that there is a moderate association between the categories.
If the Cramer’s V value is greater than 0.30, it is said that there is a strong association between the categories.
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.
For table larger than
Where,
N is the total number of elements,
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, 538 for column marginal and 748 for N in equation
Substitute 338 for row marginal, 100 for column marginal and 748 for N in equation
Substitute 338 for row marginal, 110 for column marginal and 748 for N in equation
Substitute 410 for row marginal, 538 for column marginal and 748 for N in equation
Substitute 410 for row marginal, 100 for column marginal and 748 for N in equation
Substitute 410 for row marginal, 110 for column marginal and 748 for N in equation
Consider the following table,
289  243 
(b)
To find:
The column percentages, strength and pattern of relationship.
(c)
To find:
The column percentages, strength and pattern of relationship.
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