a. Is there a statistically significant relationship between the quality of a school system and the affluence of the community as measured by per capita income?
b. Compute column percentages. Are high or low income communities more likely to have highquality schools?
Quality  Per Capita income  
Low  High  Totals  
Low  16  8  24 
High Totals 



(a)
To find:
The chi square value for the given information and test for its significance.
Given:
The given statement is,
The state Department of Education has rated a sample of local school systems for compliance with statemandated guidelines for quality.
The given table of information is,
Quality  Per Capita income  
Low  High  Totals  
Low  16  8  24 
High  9  17  26 
Totals  25  25  50 
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 24 for row marginal, 25 for column marginal and 50 for N in equation
Substitute 24 for row marginal, 25 for column marginal and 50 for N in equation
Substitute 26 for row marginal, 25 for column marginal and 50 for N in equation
Substitute 26 for row marginal, 25 for column marginal and 50 for N in equation
Consider the following table,
16  12  4  16  1 
(b)
To explain:
The given statement.
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