On an international exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in the exam, the correlation betwe the percentage of items answered in the background questionnaire (used as a proxy for student task persistence) and mean score on the exam was 0.822. Does this suggest there is a linear relation between student task persistence and achievement score? Write a sentence that explains what this result might mean. E Click the icon to view the critical values table. Does this suggest there is a linear relation between student task persistence and achievement score? Choose the best response below. O A. No, since |0.822| is less than the critical value for 30. O B. Yes, since |0.822| is less than the critical value for 30. O C. No, since |0.822| is greater than the critical value for 30. O D. Yes, since |0.822| is greater than the critical value for 30. What does this result mean? O A. Countries in which students answered a lesser percentage of items in the background questionnaire tended to have higher mean scores on the exam.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Topic Video
Question
On an international exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in the exam, the correlation between the percentage of items answered in the background questionnaire (used as a proxy for student task persistence) and mean score on the exam was 0.822. Does this suggest there is a linear relation between student task persistence and achievement score? Write a sentence that explains what this result might mean.

Click the icon to view the critical values table.

**Does this suggest there is a linear relation between student task persistence and achievement score? Choose the best response below.**

- A. No, since |0.822| is less than the critical value for 30.
- B. Yes, since |0.822| is less than the critical value for 30.
- C. No, since |0.822| is greater than the critical value for 30.
- D. Yes, since |0.822| is greater than the critical value for 30.

**What does this result mean?**

- A. Countries in which students answered a lesser percentage of items in the background questionnaire tended to have higher mean scores on the exam.
- B. Countries in which students answered a greater percentage of items in the background questionnaire tended to have higher mean scores on the exam.
- C. There is no linear relation between countries in which students answered a greater percentage of items in the background questionnaire and higher mean scores on the exam.
- D. Countries in which students cheated on the exam also cheated on the items in the background questionnaire.

Click to select your answer.
Transcribed Image Text:On an international exam, students are asked to respond to a variety of background questions. For the 41 nations that participated in the exam, the correlation between the percentage of items answered in the background questionnaire (used as a proxy for student task persistence) and mean score on the exam was 0.822. Does this suggest there is a linear relation between student task persistence and achievement score? Write a sentence that explains what this result might mean. Click the icon to view the critical values table. **Does this suggest there is a linear relation between student task persistence and achievement score? Choose the best response below.** - A. No, since |0.822| is less than the critical value for 30. - B. Yes, since |0.822| is less than the critical value for 30. - C. No, since |0.822| is greater than the critical value for 30. - D. Yes, since |0.822| is greater than the critical value for 30. **What does this result mean?** - A. Countries in which students answered a lesser percentage of items in the background questionnaire tended to have higher mean scores on the exam. - B. Countries in which students answered a greater percentage of items in the background questionnaire tended to have higher mean scores on the exam. - C. There is no linear relation between countries in which students answered a greater percentage of items in the background questionnaire and higher mean scores on the exam. - D. Countries in which students cheated on the exam also cheated on the items in the background questionnaire. Click to select your answer.
### Critical Values for Correlation Coefficient

This table provides critical values for the correlation coefficient, denoted as \( n \). The correlation coefficient measures the strength and direction of a linear relationship between two variables.

| n  | Critical Value |
|----|----------------|
| 3  | 0.997          |
| 4  | 0.950          |
| 5  | 0.878          |
| 6  | 0.811          |
| 7  | 0.754          |
| 8  | 0.707          |
| 9  | 0.666          |
| 10 | 0.632          |
| 11 | 0.602          |
| 12 | 0.576          |
| 13 | 0.553          |
| 14 | 0.532          |
| 15 | 0.514          |
| 16 | 0.497          |
| 17 | 0.482          |
| 18 | 0.468          |
| 19 | 0.456          |
| 20 | 0.444          |
| 21 | 0.433          |
| 22 | 0.423          |
| 23 | 0.413          |
| 24 | 0.404          |
| 25 | 0.396          |
| 26 | 0.388          |
| 27 | 0.381          |
| 28 | 0.374          |
| 29 | 0.367          |
| 30 | 0.361          |

#### Explanation:
The table lists sample sizes (\( n \)) from 3 to 30 alongside their corresponding critical values for the correlation coefficient. These critical values are thresholds which the sample correlation coefficient must exceed in order to be considered statistically significant at a certain confidence level. The values decrease as the sample size increases, reflecting the fact that larger samples can detect smaller effects with statistical significance.
Transcribed Image Text:### Critical Values for Correlation Coefficient This table provides critical values for the correlation coefficient, denoted as \( n \). The correlation coefficient measures the strength and direction of a linear relationship between two variables. | n | Critical Value | |----|----------------| | 3 | 0.997 | | 4 | 0.950 | | 5 | 0.878 | | 6 | 0.811 | | 7 | 0.754 | | 8 | 0.707 | | 9 | 0.666 | | 10 | 0.632 | | 11 | 0.602 | | 12 | 0.576 | | 13 | 0.553 | | 14 | 0.532 | | 15 | 0.514 | | 16 | 0.497 | | 17 | 0.482 | | 18 | 0.468 | | 19 | 0.456 | | 20 | 0.444 | | 21 | 0.433 | | 22 | 0.423 | | 23 | 0.413 | | 24 | 0.404 | | 25 | 0.396 | | 26 | 0.388 | | 27 | 0.381 | | 28 | 0.374 | | 29 | 0.367 | | 30 | 0.361 | #### Explanation: The table lists sample sizes (\( n \)) from 3 to 30 alongside their corresponding critical values for the correlation coefficient. These critical values are thresholds which the sample correlation coefficient must exceed in order to be considered statistically significant at a certain confidence level. The values decrease as the sample size increases, reflecting the fact that larger samples can detect smaller effects with statistical significance.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Centre, Spread, and Shape of a Distribution
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman