   # S O C 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. 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 4 12 8 13 12 25 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 10, Problem 10.4P
Textbook Problem
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## S O C 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.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 LowTotals 4 12 8 13 12 25

To determine

(a)

To find:

The chi square value for the given information and test for its significance.

### Explanation of Solution

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 fe is given as,

fe=Rowmarginal×ColumnmarginalN

Where N is the total of frequencies.

The chi square statistic is given by,

χ2(obtained)=(fofe)2fe

Where fo is the observed frequency,

And fe is the expected frequency.

The degrees of freedom for the bivariate table is given as,

df=(r1)(c1)

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,

fe=Rowmarginal×ColumnmarginalN.....(1)

Substitute 13 for row marginal, 12 for column marginal and 26 for N in equation (1).

f1=13×1225=6.24

Substitute 13 for row marginal, 13 for column marginal and 26 for N in equation (1).

f2=13×1325=6.76

Substitute 12 for row marginal, 12 for column marginal and 26 for N in equation (1).

f3=12×1225=5.76

Substitute 12 for row marginal, 13 for column marginal and 26 for N in equation (1).

f4=12×1325=6.24

Consider the following table,

 6.25 fo fe fo−fe (fo−fe)2 (fo−fe)2/fe 8 6.24 1.76 3.1 0.50 5 6.76 −1.76 3.1 0.46 4 5.76 −1.76 3.1 0.54 8 6.24 1.76 3.1 0.50 Total 25 25 0 χ2=2
To determine

(b)

To explain:

The given statement.

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