a. Is there a relationship between these variables? Do cities with higher homicide rates have significantly higher handgun sales? Explain your results in a sentence or two, citing both the results of the chi square test and the patterns of the column percentages.
b. The table is constructed assuming that homicide rate is the independent variable (“higher homicide rates cause people to buy more guns”). Can you think of an argument that would make handgun sales the independent variable? Which is the more logical argument? Why?
Volume of Handgun Sales  Homicide Rate  
Low  High  Totals  
High  8  5  13 
Low Totals 



(a)
To find:
The chi square value for the given information and test for its significance.
Given:
The given statement is,
A sample of 25 cities have been classified as high or low on their homicide rates and on the number of handguns sold within the city limits.
The given table of information is,
Volume of Handgun Sales  Homicide Rate  
Low  High  Totals  
High  8  5  13 
Low  4  8  12 
Totals  12  13  25 
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 13 for row marginal, 12 for column marginal and 26 for N in equation
Substitute 13 for row marginal, 13 for column marginal and 26 for N in equation
Substitute 12 for row marginal, 12 for column marginal and 26 for N in equation
Substitute 12 for row marginal, 13 for column marginal and 26 for N in equation
Consider the following table,
8  6.24  1.76  3.1  0.50  
5  6.76  3.1  0.46  
4  5.76  3.1  0.54  
8  6.24  1.76  3.1  0.50  
Total  25  25  0 
(b)
To explain:
The given statement.
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