91Ó°ÊÓ

The paper "The Relationship Between Cell Phone Use, Academic Performance, Anxiety, and Satisfaction with Life in College Students" (Computers in Human Behavior [2014]: \(343-350\) ) described a study of cell phone use among undergraduate college students at a large, Midwestern public university. The paper reported that the value of the correlation coefficient between \(x=\) Cell phone use (measured as total amount of time (in hours) spent using a cell phone on a typical day) and \(y=\) GPA (cumulative grade point average (GPA) determined from university records) was \(r=-0.203\) a. Interpret the given value of the correlation coefficient. Does the value of the correlation coefficient suggest that students who use a cell phone for more hours per day tend to have higher GPAs or lower GPAs? b. The study also investigated the correlation between texting (measured as the total number of texts sent and texts received per day) and GPA. The direction of the relationship between texting and GPA was the same as the direction of the relationship between cell phone use and GPA, but the relationship between texting and GPA was not as strong. Which of the following possible values for the correlation coefficient between texting and GPA could have been the one observed? \(r=-0.30 \quad r=-0.10 \quad r=0.10 \quad r=0.30\) c. The paper included the following statement: "Participants filled in two blanks- one for texts sent and one for texts received. These two texting items were nearly perfectly correlated." Do you think that the value of the correlation coefficient for texts sent and texts received was close to \(-1,\) close to \(0,\) or close to + 1 ? Explain your reasoning.

Step by step solution

01

a. Interpret the correlation coefficient between Cell phone use and GPA

The correlation coefficient, \(r\), measures the strength and direction of a linear relationship between two variables. In this case, \(r = -0.203\) is the correlation coefficient between Cell phone use and GPA. Since the value of `r` is negative, it indicates a weak negative linear relationship between the two variables. This means that as the Cell phone use (in hours) increases, the GPA tends to decrease, and vice versa.

02

a. Higher or Lower GPA for students with more cell phone usage

Since there is a weak negative correlation between Cell phone use and GPA, the more the hours a student uses a cell phone, the lower their GPA tends to be, and vice versa (the lower the hours spent on cell phone usage, the higher the GPA).

03

b. Possible correlation coefficient values for Texting and GPA

The correlation between texting and GPA should be in the same direction (i.e., negative) but weaker than the correlation between cell phone use and GPA. From the given values of correlation coefficients, we can choose \(r = -0.10\) as it's negative like the correlation between cell phone use and GPA, and less in absolute terms than \(r = -0.203\) (thus weaker).

04

c. Correlation coefficient value for texts sent and texts received

Since the paper states that "These two texting items were nearly perfectly correlated," this implies that there is a very strong linear relationship between texts sent and texts received. A correlation coefficient of -1 indicates a perfect negative linear relationship, 0 indicates no relationship, and +1 indicates a perfect positive linear relationship. In this case, we can conclude that the value of the correlation coefficient between texts sent and texts received is close to +1 since they would be increasing together, and as one increases, so does the other one.

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.

Correlation Coefficient

The correlation coefficient, often represented by the letter \(r\), is a statistic that quantifies the strength and direction of a linear relationship between two variables. This value ranges between -1 and 1. - An \(r\) value close to +1 indicates a strong positive linear relationship, meaning as one variable increases, the other increases too. - An \(r\) value close to -1 suggests a strong negative linear relationship, meaning as one variable increases, the other decreases. - An \(r\) value near 0 indicates no linear relationship between the variables.
In our specific study, we have \(r = -0.203\) for cell phone use and GPA. This correlation coefficient tells us that there is a weak negative relationship between these two variables. As cell phone use increases, GPA tends to decrease slightly. Though this suggests a trend, it's important to note it is weak, meaning many other factors could be at play.

Linear Relationship

A linear relationship describes a situation where two variables change in relation to each other in a consistent manner. This can be represented by a straight line on a graph. In the context of our study on college students, the linear relationship between cell phone usage and GPA was weak and negative. Despite this negative slope, the relationship is still linear because it consistently depicts that for every additional hour spent on a cell phone, GPA tends to slightly drop.
Linear relationships are foundational in statistics because they allow us to predict or understand changes in one variable as another changes. However, the strength of the linear relationship—indicated by the correlation coefficient—can greatly affect the reliability of this prediction.

Negative Correlation

Negative correlation refers to the relationship between two variables when an increase in one variable is associated with a decrease in the other. A perfect negative correlation, represented by \(r = -1\), shows that every increase in one variable results in an equivalent decrease in the other. Conversely, when \(r = -0.203\) as in our study of college students' cell phone behavior and GPA, the negative correlation is present but weak.

• This suggests that students who spend more time on their phones tend to have slightly lower GPAs.
• It's important to consider the cause-and-effect implications carefully; correlation does not imply causation.

Always remember that negative correlation, even when weak, highlights a noteworthy trend worth investigating further.

Texting Behavior in College Students

In the study mentioned, the focus was on how technology habits, such as texting, correlate with academic performance—a pressing concern among modern educators. When exploring the correlation between texting frequency and GPA, a similar negative relationship was found, albeit weaker than that of general phone use.- Choosing \(r = -0.10\) as the correlation coefficient highlights this weaker negative relationship.
This indicates that excessive texting might similarly contribute to lower GPAs, though again, the impact is less pronounced. This distinction is crucial as it suggests that different aspects of phone use might affect academic performance in varied ways.
Furthermore, texting showed a strong positive correlation between texts sent and texts received, suggesting a balanced two-way interaction, unlike the impact on GPA. Understanding these nuances can help educators and students devise better strategies for managing technology usage.