Satisfaction  Quality of life  
Low  Moderate  High  Totals  
Low  21  15  6  42 
Moderate  12  25  21  58 
High Totals 




To find:
The chi square value for the given information and test for its significance.
Given:
The given statement is,
An urban planning commissioner has created a database describing a sample of the neighborhoods in her city and has developed a scale by which each area can be rated for the “quality of life" (this includes measures of pollution, noise, open space, services available, and so on). She has also asked samples of residents of these areas about their level of satisfaction with their neighborhoods.
The given table of information is,
Satisfaction  Quality of Life  
Low  Moderate  High  Totals  
Low  21  15  6  42 
Moderate  12  25  21  58 
High  8  17  32  57 
Totals  41  57  59  157 
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 42 for row marginal, 41 for column marginal and 157 for N in equation
Substitute 42 for row marginal, 57 for column marginal and 157 for N in equation
Substitute 42 for row marginal, 59 for column marginal and 157 for N in equation
Substitute 58 for row marginal, 41 for column marginal and 157 for N in equation
Substitute 58 for row marginal, 57 for column marginal and 157 for N in equation
Substitute 58 for row marginal, 59 for column marginal and 157 for N in equation
Substitute 57 for row marginal, 41 for column marginal and 157 for N in equation
Substitute 57 for row marginal, 57 for column marginal and 157 for N in equation
Substitute 57 for row marginal, 59 for column marginal and 157 for N in equation
Consider the following table,
21  10 
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