(a) Suppose n= 6 and the sample correlation coefficient is r= 0.892. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) critical t Conclusion: O Yes, the correlation coefficient p is significantly different from 0 at the 0.01 level of significance. O No, the correlation coefficient p is not significantly different from 0 at the 0.01 level of significance. (b) Suppose n 10 and the sample correlation coefficient is r- 0.892. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) t- critical t Conclusion: O Yes, the correlation coefficient p is significantly different from 0 at the 0.01 level of significance. O No, the correlation coefficient p is not significantly different from 0 at the 0.01 level of significance. important role in determining the significance of a correlation coefficient? Explai (c) Explain why the test results of parts (a) and (b) are different even though the sample correlation coefficient r= 0.892 is the same in both parts. Does it appear that sample size plays O As n increases, so do the degrees of freedom, and the test statistic. This produces a smaller P value. O As n increases, the degrees of freedom and the test statistic decrease. This produces a smaller P value. O As n decreases, the degrees of freedom and the test statistic increase. This produces a smaller P value. O As n increases, so do the degrees freedom, and the test statistic. This produces a larger P value.
(a) Suppose n= 6 and the sample correlation coefficient is r= 0.892. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) critical t Conclusion: O Yes, the correlation coefficient p is significantly different from 0 at the 0.01 level of significance. O No, the correlation coefficient p is not significantly different from 0 at the 0.01 level of significance. (b) Suppose n 10 and the sample correlation coefficient is r- 0.892. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) t- critical t Conclusion: O Yes, the correlation coefficient p is significantly different from 0 at the 0.01 level of significance. O No, the correlation coefficient p is not significantly different from 0 at the 0.01 level of significance. important role in determining the significance of a correlation coefficient? Explai (c) Explain why the test results of parts (a) and (b) are different even though the sample correlation coefficient r= 0.892 is the same in both parts. Does it appear that sample size plays O As n increases, so do the degrees of freedom, and the test statistic. This produces a smaller P value. O As n increases, the degrees of freedom and the test statistic decrease. This produces a smaller P value. O As n decreases, the degrees of freedom and the test statistic increase. This produces a smaller P value. O As n increases, so do the degrees freedom, and the test statistic. This produces a larger P value.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Correlation Significance Testing
#### (a) Testing for Significance with Sample Size \( n = 6 \)
Given:
- Sample correlation coefficient \( r = 0.892 \)
Question: Is \( r \) significant at the 1% level of significance (two-tailed test)?
- Critical \( t = \) [Input required]
**Conclusion Options:**
- Yes, the correlation coefficient \( \rho \) is significantly different from 0 at the 0.01 level of significance.
- No, the correlation coefficient \( \rho \) is not significantly different from 0 at the 0.01 level of significance.
---
#### (b) Testing for Significance with Sample Size \( n = 10 \)
Given:
- Sample correlation coefficient \( r = 0.892 \)
Question: Is \( r \) significant at the 1% level of significance (two-tailed test)?
- Critical \( t = \) [Input required]
**Conclusion Options:**
- Yes, the correlation coefficient \( \rho \) is significantly different from 0 at the 0.01 level of significance.
- No, the correlation coefficient \( \rho \) is not significantly different from 0 at the 0.01 level of significance.
---
#### (c) Effect of Sample Size on Test Results
Question: Why are the test results of parts (a) and (b) different despite having the same sample correlation coefficient \( r = 0.892 \)?
Does sample size play an important role in determining the significance of a correlation coefficient? Explain.
**Options:**
- As \( n \) increases, so do the degrees of freedom, and the test statistic. This produces a smaller \( P \) value.
- As \( n \) increases, the degrees of freedom and the test statistic decrease. This produces a smaller \( P \) value.
- As \( n \) decreases, the degrees of freedom and the test statistic increase. This produces a smaller \( P \) value.
- As \( n \) increases, so do the degrees of freedom, and the test statistic. This produces a larger \( P \) value.
---
### Explanation
- **Graph/Diagram Explanation:**
No graphs or diagrams are present in the content provided to describe. It is focused on textual analysis of correlation significance testing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5422827a-7860-4e7c-8a0f-f4498bf171e7%2Fd4969c90-29c0-470a-973c-3d5e82b0b07f%2Fnfkjvo5_processed.png&w=3840&q=75)
Transcribed Image Text:### Correlation Significance Testing
#### (a) Testing for Significance with Sample Size \( n = 6 \)
Given:
- Sample correlation coefficient \( r = 0.892 \)
Question: Is \( r \) significant at the 1% level of significance (two-tailed test)?
- Critical \( t = \) [Input required]
**Conclusion Options:**
- Yes, the correlation coefficient \( \rho \) is significantly different from 0 at the 0.01 level of significance.
- No, the correlation coefficient \( \rho \) is not significantly different from 0 at the 0.01 level of significance.
---
#### (b) Testing for Significance with Sample Size \( n = 10 \)
Given:
- Sample correlation coefficient \( r = 0.892 \)
Question: Is \( r \) significant at the 1% level of significance (two-tailed test)?
- Critical \( t = \) [Input required]
**Conclusion Options:**
- Yes, the correlation coefficient \( \rho \) is significantly different from 0 at the 0.01 level of significance.
- No, the correlation coefficient \( \rho \) is not significantly different from 0 at the 0.01 level of significance.
---
#### (c) Effect of Sample Size on Test Results
Question: Why are the test results of parts (a) and (b) different despite having the same sample correlation coefficient \( r = 0.892 \)?
Does sample size play an important role in determining the significance of a correlation coefficient? Explain.
**Options:**
- As \( n \) increases, so do the degrees of freedom, and the test statistic. This produces a smaller \( P \) value.
- As \( n \) increases, the degrees of freedom and the test statistic decrease. This produces a smaller \( P \) value.
- As \( n \) decreases, the degrees of freedom and the test statistic increase. This produces a smaller \( P \) value.
- As \( n \) increases, so do the degrees of freedom, and the test statistic. This produces a larger \( P \) value.
---
### Explanation
- **Graph/Diagram Explanation:**
No graphs or diagrams are present in the content provided to describe. It is focused on textual analysis of correlation significance testing.
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