Recidivist?  Status  
Nonparticipant  Participant  Totals  
Yes  60  123  183 
No Totals 



To find:
The chi square value for the given information and test for its significance.
Given:
The given statement is,
A local judge has been allowing some individuals convicted of “driving under the influence” to work in a hospital emergency room as an alternative to fines, suspensions, and other penalties. A random sample of offenders has been drawn.
The given table of information is,
Recidivist?  Status  
Nonparticipants  Participant  Totals  
Yes  60  123  183 
No  55  108  163 
Totals  115  231  346 
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 183 for row marginal, 115 for column marginal and 346 for N in equation
Substitute 183 for row marginal, 231 for column marginal and 346 for N in equation
Substitute 163 for row marginal, 115 for column marginal and 346 for N in equation
Substitute 163 for row marginal, 231 for column marginal and 346 for N in equation
Consider the following table,
60  60.82  0.67  0.011  
123  122.18  0.82  0.67  0.006  
55  54.18  0.82  0.67  0.012  
108  108.82  0.67  0 
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