Salary  Status  
Union  NonUnion  Totals  
High  21  29  50 
Low Totals 



To find:
The chi square value for the given information and test for its significance.
Given:
The given statement is,
The following data represent this relationship for fire departments in a random sample of 100 cities of roughly the same size.
The given table of information is,
Salary  Status  
Union  NonUnion  Totals  
High  21  29  50 
Low  14  36  50 
Totals  35  65  100 
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 observed frequency is given as,
Substitute 50 for row marginal, 35 for column marginal and 100 for N in equation
Substitute 50 for row marginal, 65 for column marginal and 100 for N in equation
Substitute 50 for row marginal, 35 for column marginal and 100 for N in equation
Substitute 50 for row marginal, 65 for column marginal and 100 for N in equation
Consider the following table,
21  17.5  3.5  12.25  0.70  
29  32.5  12.25  0.38  
14  17.5  12.25  0.70  
36  32.5  3.5  12.25  0.38  
Total  100  100  0 
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