GPA  Residential Status  
Off Campus with Roommates  Off Campus with Parents  On Campus  Totals  
Low  22  20  48  90 
Moderate  36  40  54  130 
High Totals 




To find:
The chi square value for the given information and test for its significance.
Given:
The given statement is,
The necessary information has been collected from a random sample of 100 respondents drawn from a local community.
The given table of information is,
GPA  Residential Status  
Off Campus with Roommates  Off Campus with Parents  On Campus  Totals  
Low  22  20  48  90 
Moderate  36  40  54  130 
High  32  10  38  80 
Totals  90  70  140  300 
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 90 for row marginal, 90 for column marginal and 300 for N in equation
Substitute 90 for row marginal, 70 for column marginal and 300 for N in equation
Substitute 90 for row marginal, 38 for column marginal and 300 for N in equation
Substitute 130 for row marginal, 90 for column marginal and 300 for N in equation
Substitute 130 for row marginal, 70 for column marginal and 300 for N in equation
Substitute 130 for row marginal, 140 for column marginal and 300 for N in equation
Substitute 80 for row marginal, 90 for column marginal and 300 for N in equation
Substitute 80 for row marginal, 70 for column marginal and 300 for N in equation
Substitute 80 for row marginal, 140 for column marginal and 300 for N in equation
Consider the following table,
22  27  25  0 
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