A sample of 25 cities have been classified as high or low on their homicide rates and on the number of handgun sold within the city limits. a. Is there a relationship between these variables? b. 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 percentage. c. Assuming there is a relationship, what is the strength of this relationship? Volume of Gun Sales Homicide Rate Homicide Rate Totals Low High High 8 5 13 Low 4 8 12 Totals 12 13 25CHAPTER 10 HYPOTHESIS TESTING IV 275 Applying Statistics 10.1 The Chi Square Test Do men and women vary in their opinions about cohabita- tion? A random sample of 47' males and females has been rated as high or low in their support for \"living together.\" The results are as follows: Gender SupportforCohabitalion Male Female Totals 15 5 20 e .2 a 25 22 47 The expected frequencies are calculated cell-by-cell using Formula 10.2. Double-check to make sure that you have the correct row and column marginal when calculat- ing expected frequencies. Gender SupportforCohabitalion Male Female Totals High 10.64 9.36 20 Low 14.36 12.64 5 Totals 25 22 47 Organize the calculations of chi square with a computa- tional table. (1) (2) (3) (4) (5) Step 2. Stating the Null Hypothesis. Ho: The two variables are independent. (HI: The two variables are dependent.) Step 3. Selecting the Sampling Distribution and Estab- lishing the Critical Region. Sampling distribution = X2 distribution Alpha = 0.05 Degrees of freedom = l X2[critical) = 3.341 Step 4. Computing the Test Statistic. (f. ff f. x2(obtained) = 2 )obtained) = 6.64 Step 5. Making a Decision and Interpreting the Results of the Test. The obtained chi square is in the critical region, so we reject the null hypothesis of independence. For this sample there is a statistically signicant relation- ship between gender and support for cohabitation. Which gender is more supportive of cohabitation? We can answer this question with column percentages: s s ss eoz soa 15 10.64 4.36 19.01 1.79 5 9.36 4.36 19.01 2.03 10 14.36 4.36 19.01 1.32 E .32 i mm ya 47 47.00 0.00 f(obtained)=6.64 Step 1. Making Assumptions and Meeting Test Requirements. Model: Independent random samples Level of measurement is nominal Support for Gender Cohabitation Male High 60.00% Low 40.00% Totals 100 .00% Totals 42.55% 57.45% 100.00% Female 22.73% 77.27% 100.00% The column percentages show that 60% of males in this sample are highly supportive versus only 23% of females. We have already concluded that the relationship is sig- nicant, and now we know the pattern of the relationship: Males are more supportive