# 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

### Essentials Of Statistics

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

Chapter
Section

### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 10, Problem 10.15P
Textbook Problem
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## 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 ObamaTotals 200 365 210 383 410 748 b. Presidential preference and race/ethnicity Preference Race/Ethnicity White Black Latino Totals Romney 289 5 44 338 ObamaTotals 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 ObamaTotals 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 ObamaTotals 245 410 55 165 20 30 60 88 30 55 410 748

To determine

(a)

To find:

The chi square value for the given information and test for its significance.

### 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 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 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.

Calculation:

From the given information,

The observed frequency is given as,

fe=Rowmarginal×ColumnmarginalN ……(1)

Substitute 338 for row marginal, 365 for column marginal and 748 for N in equation (1).

f1=338×365748=164.93

Substitute 338 for row marginal, 383 for column marginal and 748 for N in equation (1).

f2=338×383748=173.07

Substitute 410 for row marginal, 365 for column marginal and 748 for N in equation (1).

f3=410×365748=200.07

Substitute 410 for row marginal, 383 for column marginal and 748 for N in equation (1).

f4=410×383748=209.93

Consider the following table,

 fo fe fo−fe (fo−fe)2 (fo−fe)2/fe 165 164.93 0.07 0.0049 0.00 173 173.07 −0.07 0.0049 0.00 200 200.07 −0.07 0.0049 0.00 210 209.93 0.07 0.0049 0.00 Total 748 748 0 χ2=0
To determine

(b)

To find:

The chi square value for the given information and test for its significance.

To determine

(c)

To find:

The chi square value for the given information and test for its significance.

To determine

(d)

To find:

The chi square value for the given information and test for its significance.

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