91Ó°ÊÓ

Speeding Tickets College students who were drivers were asked if they had ever received a speeding ticket (yes or no). The results are shown in the table, along with gender. a. There are two variables in the table, state what they are and whether each is categorical or numerical. b. Make a two-way table of the results with Male and Female across the top and Yes and No at the left edge. c. Compare the percentages of men and women who have received speeding tickets. $$ \begin{array}{|c|c|c|c|} \hline \text { Gender } & \text { Ticket } & \text { Gender } & \text { Ticket } \\ \hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{y} \\ \hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{y} \\ \hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\ \hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\ \hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\ \hline \mathrm{m} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\ \hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\ \hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\ \hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\ \hline \mathrm{m} & \mathrm{n} & \mathrm{f} & \mathrm{n} \\ \hline \mathrm{f} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\ \hline \mathrm{f} & \mathrm{y} & \mathrm{f} & \mathrm{n} \\ \hline \mathrm{f} & \mathrm{y} & & \\ \hline \end{array} $$

Step by step solution

01

Identify Variables

The two variables given in the table are 'Gender' and 'Ticket'. Both of these variables are categorical. 'Gender' has categories 'Male (m)' and 'Female (f)'. 'Ticket' has categories 'Yes (y)' and 'No (n)' which indicate whether a student has received a speeding ticket.

02

Create Two-Way Table

A two-way table is created by cross-tabulating the two categorical variables. | | Male | Female ||-------|------|--------|| Yes | 4 | 5 || No | 4 | 9 |The numbers in the cells are counts of students falling in the relevant categories.

03

Calculate Percentages

Calculating percentages of males and females who have received speeding tickets. For males: \(\frac{4}{8} * 100 = 50\% \)For females: \(\frac{5}{14} * 100 = 35.71\% \)

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.

Categorical Variables

In this exercise, you're working with two critical variables: 'Gender' and 'Ticket'. These are known as categorical variables because they represent categories or groups. Categorical variables do not take numerical values; instead, they tell us which category an observation belongs to. Here:

• 'Gender' is categorized into male (m) and female (f).
• 'Ticket' is categorized into yes (y), indicating a speeding ticket was received, and no (n), indicating it was not.

Understanding categorical variables is essential because they help us group and analyze data to reveal patterns and trends. In this exercise, such analysis allows us to see how gender is associated with receiving speeding tickets.

Gender Analysis

Analyzing the data by gender helps us see patterns or differences between male and female students regarding receiving speeding tickets. When you construct the two-way table, it helps visualize the comparison more clearly. For example:

• The total number of males surveyed was 8, with 4 having received a speeding ticket.
• The total number of females surveyed was 14, with 5 having received a speeding ticket.

By understanding these figures, we can perform further gender analysis, such as comparing the proportions of males and females who have received tickets. Thus, it's more than just counting; it's about seeing the relation between gender and the likelihood of receiving a ticket.

Descriptive Statistics

Descriptive statistics allow us to succinctly summarize and describe the key features of the collected data. In this scenario, calculating percentages for each gender group provides a clearer picture of the distribution of speeding tickets.Let’s break down the calculations:

• For males: There are a total of 8 males, and 4 have received speeding tickets. The percentage is calculated as \( \frac{4}{8} \times 100 = 50\%% \).
• For females: There are a total of 14 females, and 5 have received speeding tickets. The calculation is \( \frac{5}{14} \times 100 \approx 35.71\%% \).

These percentages make it easier to compare the likelihood of receiving a ticket between genders and understand trends within the data.