/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 7 In a study of 200 Division I ath... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

In a study of 200 Division I athletes, variables related to academic performance were examined. The paper "Noncognitive Predictors of Student Athletes' Academic Performance"' (journal of College Reading and Learning [2000]: el67) reported that the correlation coefficient for college GPA and a measure of academic self-worth was \(r=0.48\). Also reported were the correlation coefficient for college GPA and high school GPA \((r=0.46)\) and the correlation coefficient for college GPA and a measure of tendency to procrastinate \((r=-0.36) .\) Higher scores on the measure of self-worth indicate higher self-worth, and higher scores on the measure of procrastination indicate a higher tendency to procrastinate. Write a few sentences summarizing what these correlation coefficients tell you about the academic performance of the 200 athletes in the sample.

Short Answer

Expert verified
The correlation coefficient of 0.48 suggests a moderate positive relationship between college GPA and academic self-worth. The correlation coefficient of 0.46 suggests a moderate positive relationship between college GPA and high school GPA. A correlation coefficient of -0.36 indicates a moderate negative relationship between college GPA and a student's tendency to procrastinate.

Step by step solution

01

Interpret the Correlation Between College GPA and Academic Self-Worth

A correlation coefficient of 0.48 between college GPA and a measure of academic self-worth shows a moderate positive correlation. This means as academic self-worth increases, college GPA is also likely to increase.
02

Interpret the Correlation Between College GPA and High School GPA

The correlation coefficient of 0.46 between college GPA and high school GPA also suggests a moderate positive correlation. This suggests that students with higher high school GPAs also tend to have higher college GPAs.
03

Interpret the Correlation Between College GPA and Tendency to Procrastinate

The correlation coefficient of -0.36 between college GPA and a measure of tendency to procrastinate indicates a moderate negative correlation. This means that students who have a higher tendency to procrastinate tend to have lower college GPAs.

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 is a statistical measure used to evaluate the strength and direction of a linear relationship between two variables. It is usually denoted by the symbol \( r \) and ranges from -1 to 1. An \( r \) value of 1 indicates a perfect positive correlation, meaning as one variable increases, the other also increases proportionately. A value of -1 denotes a perfect negative correlation, where an increase in one variable results in a decrease in the other. An \( r \) value of 0 suggests no correlation at all, indicating no linear relationship between the variables.
For instance, in the study of Division I athletes, a correlation coefficient of 0.48 between college GPA and academic self-worth signals a moderate positive correlation between these factors. This suggests that as athletes perceive their academic self-worth positively, their college GPA tends to climb.
Similarly, a correlation coefficient of -0.36 between college GPA and procrastination indicates a moderate negative relationship. As athletes show a higher tendency to procrastinate, their college GPA is likely to drop.
Academic Performance
Academic performance, especially in studies involving athletes, often involves various metrics like GPA and personal characteristics impacting education. In the case of the Division I athletes, academic self-worth, high school GPA, and procrastination levels were analyzed.
  • Academic self-worth relates to how students perceive their ability to succeed in academic tasks. The study shows a moderate positive correlation between this perception and their college GPA, indicating confidence potentially boosts their learning outcomes.
  • High school GPA’s correlation with college GPA at 0.46 suggests past academic performance somewhat persists into higher education. This indicates a trend where students with strong high school grades continue doing well in college, but it is not a perfect predictor due to its moderate strength.
  • The negative correlation between procrastination and college GPA highlights the importance of good time management. Higher procrastination is linked to lower GPA, underscoring the detrimental effects of delaying academic responsibilities.
Understanding these relationships offers insight into improvements athletes might pursue for better academic success.
Division I Athletes
Division I athletes are individuals participating at the highest level of intercollegiate athletics sanctioned by the NCAA. Balancing sports and academics can be challenging, as these athletes often have rigorous training schedules alongside their studies.
The study of these athletes' academic performance provides insight into how their sports commitments might influence their education. The findings that academic self-worth, high school GPA, and procrastination have measurable correlations with their college GPA reveal key areas that can be focused on for enhancing their academic success.
For example, integrating programs that improve academic self-worth could coincide with improved academic results. Moreover, understanding the impact of past academic achievements and procrastination tendencies helps in crafting personalized education strategies.
Ultimately, these insights are valuable for educators, coaches, and the athletes themselves, aiming to promote a healthier balance between athletic and academic commitments, assisting athletes in reaching their fullest potential both on the field and in the classroom.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Anabolic steroid abuse has been increasing despite increased press reports of adverse medical and psychiatric consequences. In a recent study, medical researchers studied the potential for addiction to testosterone in hamsters (Neuroscience \([2004]: 971-981)\). Hamsters were allowed to self-administer testosterone over a period of days, resulting in the death of some of the animals. The data below show the proportion of hamsters surviving versus the peak self-administration of testosterone \((\mu \mathrm{g}) .\) Fit a logistic regression equation and use the equation to predict the probability of survival for a hamster with a peak intake of \(40 \mu \mathrm{g}\). \begin{tabular}{cccc} \multicolumn{4}{c} { Survival } \\ Peak Intake (micrograms) & Proportion \((p)\) & \(\frac{p}{1-p}\) & \(y^{\prime}=\ln \left(\frac{p}{1-p}\right)\) \\ \hline 10 & \(0.980\) & \(49.0000\) & \(3.8918\) \\ 30 & \(0.900\) & \(9.0000\) & \(2.1972\) \\ 50 & \(0.880\) & \(7.3333\) & \(1.9924\) \\ 70 & \(0.500\) & \(1.0000\) & \(0.0000\) \\ 90 & \(0.170\) & \(0.2048\) & \(-1.5856\) \\ \hline \end{tabular}

Cost-to-charge ratio (the percentage of the amount billed that represents the actual cost) for inpatient and outpatient services at 11 Oregon hospitals is shown in the following table (Oregon Department of Health Services, 2002 ). A scatterplot of the data is also shown. \begin{tabular}{ccc} & \multicolumn{2}{c} { Cost-to-Charge Ratio } \\ \cline { 2 - 3 } Hospital & Outpatient Care & Inpatient Care \\ \hline 1 & 62 & 80 \\ 2 & 66 & 76 \\ 3 & 63 & 75 \\ 4 & 51 & 62 \\ 5 & 75 & 100 \\ 6 & 65 & 88 \\ 7 & 56 & 64 \\ 8 & 45 & 50 \\ 9 & 48 & 54 \\ 10 & 71 & 83 \\ 11 & 54 & 100 \\ \hline \end{tabular} The least-squares regression line with \(y=\) inpatient costto-charge ratio and \(x=\) outpatient cost-to-charge ratio is \(\hat{y}=-1.1+1.29 x\). a. Is the observation for Hospital 11 an influential observation? Justify your answer. b. Is the observation for Hospital 11 an outlier? Explain. c. Is the observation for Hospital 5 an influential observation? Justify your answer. d. Is the observation for Hospital 5 an outlier? Explain.

Researchers have examined a number of climatic variables in an attempt to understand the mechanisms that govern rainfall runoff. The paper "The Applicability of Morton's and Penman's Evapotranspiration Estimates in Rainfall-Runoff Modeling" (Water 91Ó°ÊÓ Bulletin [1991]: \(611-620\) ) reported on a study that examined the relationship between \(x=\) cloud cover index and \(y=\) sunshine index. The cloud cover index can have values between 0 and \(1 .\) The accompanying data are consistent with summary quantities in the article. The authors of the article used a cubic regression to describe the relationship between cloud cover and sunshine. \begin{tabular}{cc} Cloud Cover Index \((x)\) & Sunshine Index \((y)\) \\ \hline \(0.2\) & \(10.98\) \\ \(0.5\) & \(10.94\) \\ \(0.3\) & \(10.91\) \\ \(0.1\) & \(10.94\) \\ \(0.2\) & \(10.97\) \\ \(0.4\) & \(10.89\) \\ \(0.0\) & \(10.88\) \\ \(0.4\) & \(10.92\) \\ \(0.3\) & \(10.86\) \\ \hline \end{tabular} a. Construct a scatterplot of the data. What characteristics of the plot suggest that a cubic regression would be more appropriate for summarizing the relationship between sunshine index and cloud cover index than a linear or quadratic regression? b. Find the equation of the least-squares cubic function. c. Construct a residual plot by plotting the residuals from the cubic regression model versus \(x\). Are there any troubling patterns in the residual plot that suggest that a cubic regression is not an appropriate way to summarize the relationship? d. Use the cubic regression to predict sunshine index when the cloud cover index is \(0.25\). e. Use the cubic regression to predict sunshine index when the cloud cover index is \(0.45\). f. Explain why it would not be a good idea to use the cubic regression equation to predict sunshine index for a cloud cover index of \(0.75\).

The article "Reduction in Soluble Protein and Chlorophyll Contents in a few Plants as Indicators of Automobile Exhaust Pollution" (International journal of Environmental Studies [19831: \(239-244\) ) reported the following data on \(x=\) distance from a highway (in meters) and \(y=\) lead content of soil at that distance (in parts per million): \(\begin{array}{rrrrrrr}x & 0.3 & 1 & 5 & 10 & 15 & 20 \\ y & 62.75 & 37.51 & 29.70 & 20.71 & 17.65 & 15.41 \\ x & 25 & 30 & 40 & 50 & 75 & 100 \\ y & 14.15 & 13.50 & 12.11 & 11.40 & 10.85 & 10.85\end{array}\) a. Use a statistical computer package to construct scatterplots of \(y\) versus \(x, y\) versus \(\log (x), \log (y)\) versus \(\log (x)\), and \(\frac{1}{y}\) versus \(\frac{1}{x}\) b. Which transformation considered in Part (a) does the best job of producing an approximately linear relationship? Use the selected transformation to predict lead content when distance is \(25 \mathrm{~m}\).

5.57 Does high school GPA predict success in firstyear college English? The proportion with a grade of \(C\) or better in freshman English for students with various high school GPAs for freshmen at Cal Poly, San Luis Obispo, in fall of 2007 is summarized in the accompanying table. Fit a logistic regression equation that would allow you to predict the probability of passing freshman English based on high school GPA. Use the resulting equation to predict the probability of passing freshman English for students with a high school GPA of \(2.2 .\) \begin{tabular}{cccc} High & \\ School GPA & Proportion C or Better & \(\frac{p}{1-p}\) & \(y^{\prime}=\ln \left(\frac{p}{1-p}\right)\) \\ \hline \(3.36\) & \(0.95\) & \(19.00\) & \(2.94\) \\ \(2.94\) & \(0.90\) & \(9.00\) & \(2.20\) \\ \(2.68\) & \(0.85\) & \(5.67\) & \(1.73\) \\ \(2.49\) & \(0.80\) & \(4.00\) & \(1.39\) \\ \(2.33\) & \(0.75\) & \(3.00\) & \(1.10\) \\ \(2.19\) & \(0.70\) & \(2.33\) & \(0.85\) \\ \(2.06\) & \(0.65\) & \(1.86\) & \(0.62\) \\ & & & (contimued) \end{tabular}

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.