91Ó°ÊÓ

A statistics student conducted a study on young male and female criminals 15 years of age and under who were on probation. The purpose of the study was to see whether there was an association between type of crime and gender. The subjects of the study lived in Ventura County, California. Violent crimes involve physical contact such as hitting or fighting. Nonviolent crimes are vandalism, robbery, or verbal assault. The raw data are shown in the accompanying table; \(\mathrm{v}\) stands for violent, \(\mathrm{n}\) for nonviolent, \(\mathrm{b}\) for boy, and \(\mathrm{g}\) for girl. a. Make a two-way table that summarizes the data. Label the columns (across the top) Boy and Girl. Label the rows Violent and Nonviolent. b. Find the percentage of girls on probation for violent crimes and the percentage of boys on probation for violent crimes, and compare them. c. Are the boys or the girls more likely to be on probation for violent crimes? $$\begin{array}{|c|c|} \hline \text { Gen } & \text { Viol? } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \end{array}$$ $$\begin{array}{|c|c|} \hline \text { Gen } & \text { Viol? } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { n } \\ \hline \text { b } & \text { v } \\ \hline \text { b } & \text { v } \\ \hline \text { b } & \text { v } \\ \hline \text { b } & \text { v } \\ \hline \text { b } & \text { v } \\ \hline \text { b } & \text { v } \\ \hline \text { b } & \text { v } \\ \hline \text { b } & \text { v } \\ \hline \text { b } & \text { v } \\ \hline \text { b } & \text { v } \\ \hline \text { g } & \text { n } \\ \hline \end{array}$$ $$\begin{array}{|c|c|} \hline \text { Gen } & \text { Viol? } \\ \hline \mathrm{g} & \mathrm{n} \\ \hline \mathrm{g} & \mathrm{n} \\ \hline \mathrm{g} & \mathrm{n} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \mathrm{g} & \mathrm{v} \\ \hline \end{array}$$

Step by step solution

01

Organizing the Data

The first step is to organize the data into a two-way table. From the given raw data, count the number of occurrences for each case: Girls involved in violent crimes, girls involved in nonviolent crimes, boys involved in violent crimes, and boys involved in nonviolent crimes. Let's arrange this data in a two-way table with 'Boy' and 'Girl' as column headers and 'Violent' and 'Nonviolent' as row headers.

02

Calculating the Percentages

Next, we need to find the percentage of girls and boys on probation for violent crimes. To calculate these percentages, we divide the number of violent crime cases by the total number of cases for each gender and multiply by 100.

03

Making Comparisons

Finally, we compare the percentages calculated in Step 2. The gender with the larger percentage is more likely to be on probation for violent crimes.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Association Between Variables

In statistics, understanding the association between variables is crucial for determining how one variable might influence or relate to another.
For the exercise at hand, the variables being focused on are the type of crime (violent or nonviolent) and gender (boy or girl).
By using a two-way table, we can visually represent the relationship between these categories.
The purpose of identifying associations is to assess whether there might be a pattern or a significant relation between the variables under study.

• If a notable pattern is observed between gender and crime type, it can lead to further inquiry or targeted intervention strategies.
• Statistical tools like chi-square tests can sometimes be used to test the significance of the observed associations.

The exercise seeks to determine if gender has an influence on the type of crime committed by the youths. This is a foundational step in understanding more complex relationships between variables in statistical research.

Percentages in Data

Calculating percentages is a powerful tool in statistics, especially when comparing subgroups within a dataset.
Percentages give a proportionate understanding of data, helping us simplify and interpret information quantitatively.
For the data regarding young criminals, it is essential to find out what fraction of boys and girls are involved in violent crimes compared to nonviolent ones. To determine these percentages:

• Count the total number of each gender. For instance, the total number of boys and the total number of girls in the dataset.
• Within each gender, count how many are involved in violent crimes and divide it by the total count for that gender.
• Multiply by 100 to convert this ratio into a percentage.

For example, if there are 20 boys and 15 were involved in violent crimes, the percentage of boys involved in violent crimes is: \[\frac{15}{20} \times 100 = 75\%\]Calculating and comparing these percentages gives a clearer picture of how widespread violence-related behavior is among boys and girls respectively, allowing for informed decisions or actions.

Comparative Statistics

Comparative statistics involve analyzing and interpreting data to highlight differences and similarities between groups.
In this case, the emphasis is on comparing the percentages of boys and girls engaged in violent crimes.
Once the percentages are determined, seeing which gender has a higher proportion involved in violent crimes helps address the third part of the exercise.To compare effectively:

• Determine the differential: Subtract the percentage of girls involved in violent crimes from the percentage of boys, or vice versa.
• Observe the magnitude of difference: A bigger difference might indicate a more noteworthy pattern.

Let's illustrate this with hypothetical data:

• If 75% of boys and 60% of girls are involved in violent crimes, the difference is \(75\% - 60\% = 15\%\).
• This suggests a noteworthy comparative statistic, as boys might be more inclined towards violent activities than girls.

Comparing data like this helps highlight distinct trends or disparities, making it easier to draw conclusions and possibly predict future patterns based on past data behavior.