Political Views 
Class Standing  
Freshmen and Sophomore  Junior and Senior  Totals  
Liberal  40  43  83 
Moderate  50  50  100 
Conservative Totals 



To find:
The chi square value for the given information and test for its significance.
Given:
The given statement is,
The following table reports the relationship between these two variables for a random sample of 267 college students.
The given table of information is,
Political views  Class Standing  Totals  
Freshmen and Sophomore  Juniors and seniors  
Liberal  40  43  83 
Moderate  50  50  100 
Conservative  44  40  84 
Totals  134  133  267 
Steps:
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 83 for row marginal, 134 for column marginal and 267 for N in equation
Substitute 83 for row marginal, 133 for column marginal and 267 for N in equation
Substitute 100 for row marginal, 134 for column marginal and 267 for N in equation
Substitute 100 for row marginal, 133 for column marginal and 267 for N in equation
Substitute 84 for row marginal, 134 for column marginal and 267 for N in equation
Substitute 84 for row marginal, 133 for column marginal and 267 for N in equation
Consider the following table,
40  41.66  2.76  0.066  
43  41.34  1.66  2.76  0.067  
50  50.19 
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