Gender  
Party Preference 
Male  Female  Totals 
Democrat  10  15  25 
Republican Totals 



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?
(a)
To find:
The chi square value for the given information and test for its significance.
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
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 row marginal is 25, the column marginal is 25 and N is 50.
The observed frequency is given as,
Substitute 25 for row marginal, 25 for column marginal and 50 for N in the above formula.
Consider the following table,
10  12.5  0.5  
15  12.5  0.5  
15  12.5  0.5  
10  12.5  0.5  
Total  50  50  0 
The value
Substitute 10 for
(b)
To find:
The chi square value for the given information and test for its significance.
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