Based on the information in the table above, the researchers compute the regression equation: Y = -0.970+ 0.125 X. Do the researchers have enough evidence to claim that the number of hours studying predicts students' GPA? Should you reject or fail to reject the null hypothesis? Fail to reject Reject
Based on the information in the table above, the researchers compute the regression equation: Y = -0.970+ 0.125 X. Do the researchers have enough evidence to claim that the number of hours studying predicts students' GPA? Should you reject or fail to reject the null hypothesis? Fail to reject Reject
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
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Question
![### Can Studying Hours Predict College GPA?
Researchers are investigating whether the number of hours spent studying per week can predict college GPA. For this study, they randomly selected 8 college students and recorded their GPA and the number of hours they spend studying each week. The data collected 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 |
**Analysis:**
The researchers computed the regression equation based on the collected data:
\[ \hat{Y} = -0.970 + 0.125X \]
where \(\hat{Y}\) represents the predicted GPA and \(X\) represents the number of hours spent studying per week.
**Question:**
Do the researchers have enough evidence to claim that the number of hours spent studying per week predicts students' GPA?
### Hypothesis Testing
To address this question, consider the null hypothesis: "The number of hours spent studying per week does not predict students' GPA."
**Decision:**
Should you reject or fail to reject the null hypothesis?
- ⭕ Fail to reject
- ⭕ Reject](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf10b40a-fae6-4e8b-9b89-0711a68556bc%2Ff334e55b-66cc-4126-b0e0-53b10114be75%2Fg6qbh9o_processed.png&w=3840&q=75)
Transcribed Image Text:### Can Studying Hours Predict College GPA?
Researchers are investigating whether the number of hours spent studying per week can predict college GPA. For this study, they randomly selected 8 college students and recorded their GPA and the number of hours they spend studying each week. The data collected 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 |
**Analysis:**
The researchers computed the regression equation based on the collected data:
\[ \hat{Y} = -0.970 + 0.125X \]
where \(\hat{Y}\) represents the predicted GPA and \(X\) represents the number of hours spent studying per week.
**Question:**
Do the researchers have enough evidence to claim that the number of hours spent studying per week predicts students' GPA?
### Hypothesis Testing
To address this question, consider the null hypothesis: "The number of hours spent studying per week does not predict students' GPA."
**Decision:**
Should you reject or fail to reject the null hypothesis?
- ⭕ Fail to reject
- ⭕ Reject
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