chapter 12 practice: bivariate association fo...

chapter 12 practice: bivariate association for nominal - and ordinal - level variables\n\n|enforcement action (y)|driver age (x)| | | |totals|\n|----|----|----|----|----|----|\n| |16 - 24|25 - 44|45 - 64|65 or older| |\n|ticket|268|357|446|713|1,784|\n|warning|241|157|525|126|1,049|\n|no action|332|173|73|86|664|\n|totals|841|687|1,044|925|3,497|\n\nchi square = 760.69, df = 6, p < 0.001.\n\nyou are interested in the possible association between drivers age and type of enforcement action. since this bivariate table is larger than 2 x 2, the measure phi is not appropriate. instead, you use cramers v to assess the strength of the relationship. calculate cramers v for this table. (note: the value of chi square is provided for you in the table.)\n\ncramers v = \n\nthis result indicates a relationship between drivers age and type of enforcement action.\n\nwhich of the following conclusions are valid from this analysis? check all that apply.\n\n□ there is a moderate association between the type of enforcement action at traffic stops and the age of the driver.\n□ the type of enforcement action at a traffic stop affects the drivers perception of police behavior.\n□ the age of a driver affects the enforcement decision of police at traffic stops.\n□ there is a strong association between the type of enforcement action at traffic stops and the age of the driver.

Answer

# Explanation: ## Step1: Recall Cramer's V formula $V = \sqrt{\frac{\chi^{2}}{n\times k}}$ where $\chi^{2}$ is the chi - square value, $n$ is the total number of observations, and $k$ is the minimum of the number of rows minus 1 and the number of columns minus 1 in the contingency table. The contingency table has 4 rows and 4 columns. So $k=\min(4 - 1,4 - 1)=3$, $\chi^{2}=760.69$, and $n = 3497$. ## Step2: Calculate Cramer's V $V=\sqrt{\frac{760.69}{3497\times3}}=\sqrt{\frac{760.69}{10491}}\approx\sqrt{0.0725}\approx 0.27$ ## Step3: Interpret the result A Cramer's V value of around 0.27 indicates a moderate relationship. # Answer: Cramer's V $\approx0.27$ This result indicates a moderate relationship between driver's age and type of enforcement action. Valid conclusions: - There is a moderate association between the type of enforcement action at traffic stops and the age of the driver. - The age of a driver affects the enforcement decision of police at traffic stops.