   # P S As mentioned in this chapter, many analysts have noted a “gender gap” in U.S. elections, with women more likely to vote for the Democratic candidate. A sample of university faculty has been asked about their political party preference. Do their responses indicate a significant relationship between gender and party preference for this group? Gender Party Preference Male Female Totals Democrat 10 15 25 Republican Totals 15 25 10 25 25 50 a. Is there a statistically significant relationship between gender and party preference? b. Compute column percentages for the table to clarify the pattern of the relationship. Which gender is more likely to prefer the Democrats? ### Essentials Of Statistics

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

#### Solutions

Chapter
Section ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 10, Problem 10.2P
Textbook Problem
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## P S As mentioned in this chapter, many analysts have noted a “gender gap” in U.S. elections, with women more likely to vote for the Democratic candidate. A sample of university faculty has been asked about their political party preference. Do their responses indicate a significant relationship between gender and party preference for this group? Gender PartyPreference Male Female Totals Democrat 10 15 25 RepublicanTotals 15 25 10 25 25 50 a. Is there a statistically significant relationship between gender and party preference?b. Compute column percentages for the table to clarify the pattern of the relationship. Which gender is more likely to prefer the Democrats?

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,

Women more likely to vote for the Democratic candidate.

The given table of information is,

 Gender Male Female Totals Democrat 10 15 25 Republican 15 10 25 Totals 25 25 50

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 row marginal is 25, the column marginal is 25 and N is 50.

The observed frequency is given as,

fe=Rowmarginal×ColumnmarginalN

Substitute 25 for row marginal, 25 for column marginal and 50 for N in the above formula.

fe=25×2550=12.5

Consider the following table,

 6.25 fo fe fo−fe (fo−fe)2 (fo−fe)2/fe 10 12.5 −2.5 6.25 0.5 15 12.5 2.5 6.25 0.5 15 12.5 2.5 6.25 0.5 10 12.5 −2.5 6.25 0.5 Total 50 50 0 χ2=2.0

The value fofe is obtained as,

Substitute 10 for fo and 12

To determine

(b)

To find:

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

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