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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4175707-d254-4126-a791-753312836f35%2F84e3b164-7c68-4d64-b005-8d802d5e5f81%2Fxb1fup_processed.png&w=3840&q=75)
![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4175707-d254-4126-a791-753312836f35%2F84e3b164-7c68-4d64-b005-8d802d5e5f81%2Fer4v4t_processed.png&w=3840&q=75)
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