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P S Below are some of the tables you analyzed in problem 10.17. You already have the results of the chi square tests. Now, analyze these relationships in terms of association, using an appropriate measure of association. Write a paragraph summarizing your results. a . Presidential preference and race/ethnicity Preference Race/Ethnicity White Black Latino Totals Romney 289 5 44 338 Obama Totals 249 538 95 100 66 110 410 748 b . Presidential preference by education Preference Education Less than HS HS Graduate College Graduate Post-Graduate Degree Totals Romney 30 180 118 10 338 Obama Totals 35 65 120 300 218 336 37 47 410 748 c. Presidential preference by religion Preference Religion Protestant Catholic Jewish None Other Totals Romney 165 110 10 28 25 338 Obama Totals 245 410 55 165 20 30 60 88 30 55 410 748 10.15 P S 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 200 365 210 383 410 748 b. Presidential preference and race/ethnicity Preference Race/Ethnicity White Black Latino Totals Romney 289 5 44 338 Obama Totals 249 538 95 100 66 110 410 748 c. Presidential preference by education Preference Education Less than HS HS Graduate College Graduate Post-Graduate Degree Totals Romney 30 180 118 10 338 Obama Totals 35 65 120 300 218 336 37 47 410 748 d. Presidential preference by religion Preference Religion Protestant Catholic Jewish None Other Totals Romney 165 110 10 28 25 338 Obama Totals 245 410 55 165 20 30 60 88 30 55 410 748

BuyFindarrow_forward

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

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Chapter
Section
BuyFindarrow_forward

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 11, Problem 11.5P
Textbook Problem
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P S Below are some of the tables you analyzed in problem 10.17. You already have the results of the chi square tests. Now, analyze these relationships in terms of association, using an appropriate measure of association. Write a paragraph summarizing your results.

a. Presidential preference and race/ethnicity

Preference Race/Ethnicity
White Black Latino Totals
Romney 289 5 44 338
Obama
Totals
249 538 95 100 66 110 410 748

b. Presidential preference by education

Preference Education
Less than HS HS Graduate College Graduate Post-Graduate Degree Totals
Romney 30 180 118 10 338
Obama
Totals
35 65 120 300 218 336 37 47 410 748

c. Presidential preference by religion

Preference Religion
Protestant Catholic Jewish None Other Totals
Romney 165 110 10 28 25 338
Obama
Totals
245 410 55 165 20 30 60 88 30 55 410 748

10.15 P S 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
200 365 210 383 410 748

b. Presidential preference and race/ethnicity

Preference Race/Ethnicity
White Black Latino Totals
Romney 289 5 44 338
Obama
Totals
249 538 95 100 66 110 410 748

c. Presidential preference by education

Preference Education
Less than HS HS Graduate College Graduate Post-Graduate Degree Totals
Romney 30 180 118 10 338
Obama
Totals
35 65 120 300 218 336 37 47 410 748

d. Presidential preference by religion

Preference Religion
Protestant Catholic Jewish None Other Totals
Romney 165 110 10 28 25 338
Obama
Totals
245 410 55 165 20 30 60 88 30 55 410 748

To determine

(a)

To find:

The column percentages, strength and pattern of relationship.

Explanation of Solution

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 fe is given as,

fe=Rowmarginal×ColumnmarginalN

Where N is the total of frequencies.

The chi square statistic is given by,

χ2(obtained)=(fofe)2fe

Where fo is the observed frequency,

And fe is the expected frequency.

The degrees of freedom for the bivariate table is given as,

df=(r1)(c1)

Where r is the number of rows and c is the number of columns.

For table larger than 2×2, the Cramer’s V is given by the formula,

V=χ2N(minr1,c1)

Where, χ2 is the chi square value,

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,

fe=Rowmarginal×ColumnmarginalN(1)

Substitute 338 for row marginal, 538 for column marginal and 748 for N in equation (1).

f1=338×538748=243.11

Substitute 338 for row marginal, 100 for column marginal and 748 for N in equation (1).

f2=338×100748=45.19

Substitute 338 for row marginal, 110 for column marginal and 748 for N in equation (1).

f3=338×110748=49.71

Substitute 410 for row marginal, 538 for column marginal and 748 for N in equation (1).

f4=410×538748=294.89

Substitute 410 for row marginal, 100 for column marginal and 748 for N in equation (1).

f5=410×100748=54.81

Substitute 410 for row marginal, 110 for column marginal and 748 for N in equation (1).

f6=410×110748=60.29

Consider the following table,

fo fe fofe (fofe)2 (fofe)2/fe
289 243
To determine

(b)

To find:

The column percentages, strength and pattern of relationship.

To determine

(c)

To find:

The column percentages, strength and pattern of relationship.

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