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Chapter 2: Problem 26

Use data on college students collected from the American College Health Association-National College Health Assessment survey \(^{18}\) conducted in Fall 2011 . The survey was administered at 44 colleges and universities representing a broad assortment of types of schools and representing all major regions of the country. At each school, the survey was administered to either all students or a random sample of students, and more than 27,000 students participated in the survey. Students in the ACHA-NCHA survey were asked, "Within the last 12 months, have you been in a relationship (meaning an intimate/coupled/partnered relationship) that was emotionally abusive?" The results are given in Table 2.12 . (a) What percent of all respondents have been in an emotionally abusive relationship? (b) What percent of the people who have been in an emotionally abusive relationship are male? (c) What percent of males have been in an emotionally abusive relationship? (d) What percent of females have been in an emotionally abusive relationship? Table 2.12 Have you been in an emotionally abusive relationship? $$\begin{array}{l|rr|r} \hline & \text { Male } & \text { Female } & \text { Total } \\ \hline \text { No } & 8352 & 16,276 & 24,628 \\ \text { Yes } & 593 & 2034 & 2627 \\ \hline \text { Total } & 8945 & 18,310 & 27,255 \\ \hline\end{array}$$

Short Answer

Expert verified
a) 9.64% of all respondents have been in an emotionally abusive relationship. b) 22.57% of people who have been in an emotionally abusive relationship are male. c) 6.63% of males have been in an emotionally abusive relationship. d) 11.1% of females have been in an emotionally abusive relationship.

Step by step solution

01

Calculate the total percent of all respondents having been in an abusive relationship

First, we need to calculate what percent of all respondents have been in an emotionally abusive relationship. To do this, we will divide the total number of 'yes' responses (2627) by the overall total number of respondents (27,255). Multiply the result by 100 to convert it into a percentage. i.e., \((\frac{2627}{27255}) \times 100\)
02

Calculate the percent who are male among the emotionally abused

We also need to find out what percent of those who have been in an emotionally abusive relationship are male. To do this, we will divide the number of 'yes' responses from males (593) by the total number of 'yes' responses (2627). Multiply the result by 100 to convert it into a percentage. i.e., \((\frac{593}{2627}) \times 100\)
03

Calculate the percentage of males having faced emotional abuse

Next, we need to calculate the percent of males who have been in an emotionally abusive relationship. To do this, we will divide the number of 'yes' responses from males (593) by the total number of male respondents (8945). Multiply the result by 100 to convert it into a percentage. i.e., \((\frac{593}{8945}) \times 100\)
04

Calculate the percentage of females having faced emotional abuse

Lastly, we calculate the percent of females who have been in an emotionally abusive relationship. To do this, we will divide the number of 'yes' responses from females (2034) by the total number of female respondents (18,310). Multiply the result by 100 to convert it into a percentage. i.e., \((\frac{2034}{18310}) \times 100\)

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Key Concepts

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

Understanding Emotionally Abusive Relationships
Emotionally abusive relationships can be subtle yet profoundly harmful. Recognizing these relationships involves understanding certain behavioral patterns. In such relationships, one partner may try to dominate or control the other through fear, emotional manipulation, or consistent put-downs. This can be damaging to the victim's mental and emotional wellbeing. Abuse might manifest as:
  • Isolation from friends and family
  • Demeaning language or belittlement
  • Gaslighting, where the abuser makes the victim doubt their perception or reality
  • Constant criticism or making the victim feel inadequate
Understanding the signs is the first step in seeking help and regaining control over one's life. It's essential for individuals to know that they are not alone, and many support resources are available to help them through such situations.
The Role of Data Analysis in Understanding Surveys
Data analysis plays a crucial role in understanding surveys, like the one conducted on college student relationships. In this context, analyzing data involves several steps: - **Data Collection:** Gathering information from respondents. In the given survey, data was collected from over 27,000 students across various colleges to ensure a diverse representation of the student population. - **Data Cleaning:** This process involves checking for any inconsistencies or errors in the dataset and fixing them. Ensuring data integrity is crucial for accurate analysis. - **Data Interpretation:** Once clean, the data is analyzed to make sense of the various responses. Analysts use statistical methods to draw meaningful conclusions. For example, the collected data helps in understanding the extent of emotional abuse among students and can guide institutions in creating necessary support structures. Effective data analysis is vital as it transforms raw data into actionable insights. It helps stakeholders make informed decisions to improve student welfare.
How to Calculate Percentages in Surveys
Understanding percentage calculation is crucial when interpreting survey data. Percentages help to standardize the results, making them easier to compare and understand. To calculate a percentage, you follow a few essential steps: 1. **Identify the Numbers:** Recognize the part and the whole you are interested in. For example, if you want to find the percentage of respondents who experienced abuse, identify the number of 'yes' responses and the total respondents. 2. **Perform Division:** Divide the part by the whole. In mathematical terms, if you want to find the percentage of students who reported abuse, divide the number of 'yes' responses (2627) by the total number of respondents (27,255).3. **Convert to Percentage:** Multiply the result by 100. This moves the decimal point two places to the right, converting your fraction into a percentage. So for our example, the calculation looks like this: \[ \left( \frac{2627}{27255} \right) \times 100 = 9.64\% \]By following these steps, anyone can easily ascertain percentages in survey data, allowing for a clearer understanding of the survey results. This precision is significant when evaluating sensitive topics, like the rate of emotionally abusive relationships among students.

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Most popular questions from this chapter

Multiple studies \(^{61}\) in both animals and humans show the importance of a mother's love (or the unconditional love of any close person to a child) in a child's brain development. A recent study shows that children with nurturing mothers had a substantially larger area of the brain called the hippocampus than children with less nurturing mothers. This is important because other studies have shown that the size of the hippocampus matters: People with large hippocampus area are more resilient and are more likely to be able to weather the stresses and strains of daily life. These observations come from experiments in animals and observational studies in humans. (a) Is the amount of maternal nurturing one receives as a child positively or negatively associated with hippocampus size? (b) Is hippocampus size positively or negatively associated with resiliency and the ability to weather the stresses of life? (c) How might a randomized experiment be designed to test the effect described in part (a) in humans? Would such an experiment be ethical? (d) Can we conclude that maternal nurturing in humans causes the hippocampus to grow larger? Can we conclude that maternal nurturing in animals (such as mice, who were used in many of the experiments) causes the hippocampus to grow larger? Explain.

Give the relevant proportion using correct notation. Of all 1,672,395 members of the high school class of 2014 who took the SAT (Scholastic Aptitude Test), 793,986 were minority students.

Researchers examined all sports-related concussions reported to an emergency room for children ages 5 to 18 in the United States over the course of one year. \({ }^{11}\) Table 2.7 displays the number of concussions in each of the major activity categories. (a) Are these results from a population or a sample? (b) What proportion of concussions came from playing football? (c) What proportion of concussions came from riding bicycles? (d) Can we conclude that, at least in terms of concussions, riding bicycles is more dangerous to children in the US than playing football? Why or why not? $$\begin{array}{l|r}\hline \text { Activity } & \text { Frequency } \\ \hline \text { Bicycles } & 23,405 \\ \text { Football } & 20,293 \\\\\text { Basketball } & 11,507 \\ \text { Playground } & 10,414 \\\\\text { Soccer } & 7,667 \\\\\text { Baseball } & 7,433 \\\\\text { All-Terrain Vehicle } & 5,220 \\\\\text { Hockey } & 4,111 \\\\\text { Skateboarding } & 4,408 \\\\\text { Swimming } & 3,846 \\\\\text { Horseback Riding } & 2,648 \\ \hline \text { Total } & 100,952 \\\\\hline\end{array}$$

Indicate whether the five number summary corresponds most likely to a distribution that is skewed to the left, skewed to the right, or symmetric. (15,25,30,35,45)

Exercise 2.143 on page 102 introduces a study that examines several variables on collegiate football players, including the variable Years, which is number of years playing football, and the variable Cognition, which gives percentile on a cognitive reaction test. Exercise 2.182 shows a scatterplot for these two variables and gives the correlation as -0.366 . The regression line for predicting Cognition from Years is: $$\text { Cognition }=102-3.34 \cdot \text { Years }$$ (a) Predict the cognitive percentile for someone who has played football for 8 years and for someone who has played football for 14 years. (b) Interpret the slope in terms of football and \(\operatorname{cog}-\) nitive percentile. (c) All the participants had played between 7 and 18 years of football. Is it reasonable to interpret the intercept in context? Why or why not?
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