A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Related questions
Question
![**Predicting GPA from Hours Studying: A Regression Analysis**
Researchers are investigating whether the number of hours spent studying per week can predict college GPA. To test this hypothesis, they randomly selected 8 college students, recorded their GPA and the number of hours spent studying per week. The data is summarized in the table below:
| ID | GPA | Hours studying per week |
|----|-----|-------------------------|
| 1 | 2.5 | 25.0 |
| 2 | 2.7 | 27.6 |
| 3 | 3.4 | 30.2 |
| 4 | 3.7 | 35.0 |
| 5 | 2.7 | 31.6 |
| 6 | 1.9 | 25.6 |
| 7 | 2.0 | 30.0 |
| 8 | 4.0 | 40.0 |
Based on the information in the table, the researchers computed the regression equation:
\[ \hat{Y} = -0.970 + 0.125X \]
where \( \hat{Y} \) represents the predicted GPA and \( X \) represents the hours spent studying per week.
### Research Question
Do the researchers have enough evidence to claim that the number of hours studying predicts students’ GPA?
### Statistical Test
Select the null hypothesis for the statistical test:
- \( b = 0 \)
- \( \beta = 0 \)
- \( \beta = -0.970 \)
- \( b = 0.125 \)
**Explanation of Regression Equation:**
The regression equation provided can be interpreted as follows:
- The coefficient \( 0.125 \) indicates that for each additional hour spent studying per week, the GPA is predicted to increase by 0.125, on average.
- The constant term \( -0.970 \) represents the y-intercept, which is the predicted GPA when the number of hours studying per week is zero.
**Null Hypothesis:**
To determine if the number of hours studying is a predictor of GPA, the null hypothesis \( \beta = 0 \) must be tested. This hypothesis states that the slope of the regression line is zero, meaning that there is no linear relationship between the number of hours studying and GPA. If this hypothesis is rejected](https://content.bartleby.com/qna-images/question/af10b40a-fae6-4e8b-9b89-0711a68556bc/e3d7b24a-7ec1-420d-82c0-41bbb6c64fed/3ea2hdm_processed.png)
Transcribed Image Text:**Predicting GPA from Hours Studying: A Regression Analysis**
Researchers are investigating whether the number of hours spent studying per week can predict college GPA. To test this hypothesis, they randomly selected 8 college students, recorded their GPA and the number of hours spent studying per week. The data is summarized in the table below:
| ID | GPA | Hours studying per week |
|----|-----|-------------------------|
| 1 | 2.5 | 25.0 |
| 2 | 2.7 | 27.6 |
| 3 | 3.4 | 30.2 |
| 4 | 3.7 | 35.0 |
| 5 | 2.7 | 31.6 |
| 6 | 1.9 | 25.6 |
| 7 | 2.0 | 30.0 |
| 8 | 4.0 | 40.0 |
Based on the information in the table, the researchers computed the regression equation:
\[ \hat{Y} = -0.970 + 0.125X \]
where \( \hat{Y} \) represents the predicted GPA and \( X \) represents the hours spent studying per week.
### Research Question
Do the researchers have enough evidence to claim that the number of hours studying predicts students’ GPA?
### Statistical Test
Select the null hypothesis for the statistical test:
- \( b = 0 \)
- \( \beta = 0 \)
- \( \beta = -0.970 \)
- \( b = 0.125 \)
**Explanation of Regression Equation:**
The regression equation provided can be interpreted as follows:
- The coefficient \( 0.125 \) indicates that for each additional hour spent studying per week, the GPA is predicted to increase by 0.125, on average.
- The constant term \( -0.970 \) represents the y-intercept, which is the predicted GPA when the number of hours studying per week is zero.
**Null Hypothesis:**
To determine if the number of hours studying is a predictor of GPA, the null hypothesis \( \beta = 0 \) must be tested. This hypothesis states that the slope of the regression line is zero, meaning that there is no linear relationship between the number of hours studying and GPA. If this hypothesis is rejected
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 3 steps with 6 images
Knowledge Booster
Similar questions
- A math teacher asks each student how much time they spent studying for their last math test. She then checks each student’s overall mark. Is this case an experimental study or an observational study? 1.experimental study 2.observational studyarrow_forwardWhat is the median?arrow_forwardYou want to determine how many loaves of Bread are sold per day at Schat’s Bakery. You stand outside for ten different randomly selected days, count the number of loaves, and then average them. You come up with 421 loaves per day. In reality, Schat’s keeps records of how many loaves they sell per day, and in they averaged 395 loaves per day. Describe what the population is in the above example?arrow_forward
- An instructor is wondering if students who spend more time taking their final exam do better than those who take less time. The following data is gathered. Minutes 57 47 36 83 86 117 87 62 87 86 68 106 95 72 95 Score 96 92 92 77 96 96 81 85 88 96 70 81 77 74 77 What is the coefficient of determination? Multiple Choice −0.128 0.016 0.651 −0.053arrow_forwardK A university conducted a survey of 387 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. Complete parts (a) through (d) below. Click the icon to view the table. 美 Data table Satisfied Neutral Not satisfied Total Freshman Sophomore Junior Senior 51 48 62 59 28 20 18 13 23 21 18 26 102 89 98 98 Total D₁ 220 79 88 387arrow_forwardOxygen consumption was measured in twelve individuals while they sat with their eyes closed listening to an exciting adventure story read by Taylor Swift or a restful instrumental medley performed by Metallica. Based on the results shown, is oxygen consumption less when listening to the music? Story Music 6.1 5.4 7.2 6.7 5.7 5.4 6.4 4.2 5.8 4.0 6.2 4.1arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:9780134753119
Author:Sheldon Ross
Publisher:PEARSON