The critical value are r= ____________________ (Round to three decimal places as needed. Use a comma to separate answers as needed.) Choose one right answer to match the sentence: Because the absolute value of the linear correlation coefficient is greater or less than the positive critical value, there is or is not sufficient evidence to support the claim that there is a linear correlation between the overhead widths of seals from photographs and the weights of the seals for a significant level of α = 0.05 .
The critical value are r= ____________________ (Round to three decimal places as needed. Use a comma to separate answers as needed.) Choose one right answer to match the sentence: Because the absolute value of the linear correlation coefficient is greater or less than the positive critical value, there is or is not sufficient evidence to support the claim that there is a linear correlation between the overhead widths of seals from photographs and the weights of the seals for a significant level of α = 0.05 .
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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The critical value are r= ____________________
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
Choose one right answer to match the sentence:
Because the absolute value of the linear
Transcribed Image Text:### Critical Values of the Correlation Coefficient Table
This table provides critical values of the correlation coefficient for various sample sizes (n) at significance levels of α = 0.05 and α = 0.01. It can be used to determine if a calculated correlation from a data sample is statistically significant.
| **n** | **α = 0.05** | **α = 0.01** |
|-------|--------------|--------------|
| 4 | .950 | .990 |
| 5 | .878 | .959 |
| 6 | .811 | .917 |
| 7 | .754 | .875 |
| 8 | .707 | .834 |
| 9 | .666 | .798 |
| 10 | .632 | .765 |
| 11 | .602 | .735 |
| 12 | .576 | .708 |
| 13 | .553 | .684 |
| 14 | .532 | .661 |
| 15 | .514 | .641 |
| 16 | .497 | .623 |
| 17 | .482 | .606 |
| 18 | .468 | .590 |
| 19 | .456 | .575 |
| 20 | .444 | .561 |
| 25 | .396 | .505 |
| 30 | .361 | .463 |
| 35 | .335 | .432 |
| 40 | .312 | .402 |
| 45 | .294 | .378 |
| 50 | .279 | .354 |
| 60 | .254 | .330 |
| 70 | .236 | .306 |
| 80 | .220 | .286 |
| 90 | .207 | .269 |
| 100 | .196 | .256 |
**NOTE:** To test the null hypothesis \( H_0: \rho = 0 \) against the alternative hypothesis \( H_1: \rho \neq 0 \), reject \( H_0 \
![**Seal Measurement Correlation Study**
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient \( r \), and find the critical values of \( r \) using \( \alpha = 0.05 \). Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
| Overhead Width | 7.0 | 7.8 | 9.7 | 9.3 | 8.7 | 8.4 |
|----------------|-----|-----|-----|-----|-----|-----|
| Weight | 111 | 200 | 246 | 199 | 198 | 194 |
[Click here to view a table of critical values for the correlation coefficient.]
---
**Task: Construct a Scatterplot**
Choose the correct graph below:
- **A.** Incorrect scatterplot.
- **B.** Incorrect scatterplot.
- **C.** Correct scatterplot.
- **D.** Incorrect scatterplot.
**Explanation of Correct Scatterplot (C):**
- **X-axis**: Represents the overhead width in cm (ranging from 7 to 10).
- **Y-axis**: Represents the weight in kg (ranging from 100 to 300).
- The points are plotted to show the relationship between the widths and weights of the seals.
**Question:**
Find the linear correlation coefficient \( r \).
(Provide your answer rounded to three decimal places.)
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7207ec05-c570-45c5-9f93-6adc9f301e8e%2F2fec6da0-8a79-4d59-8871-e7d4402656a7%2F3ty5bc_processed.png&w=3840&q=75)
Transcribed Image Text:**Seal Measurement Correlation Study**
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient \( r \), and find the critical values of \( r \) using \( \alpha = 0.05 \). Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?
| Overhead Width | 7.0 | 7.8 | 9.7 | 9.3 | 8.7 | 8.4 |
|----------------|-----|-----|-----|-----|-----|-----|
| Weight | 111 | 200 | 246 | 199 | 198 | 194 |
[Click here to view a table of critical values for the correlation coefficient.]
---
**Task: Construct a Scatterplot**
Choose the correct graph below:
- **A.** Incorrect scatterplot.
- **B.** Incorrect scatterplot.
- **C.** Correct scatterplot.
- **D.** Incorrect scatterplot.
**Explanation of Correct Scatterplot (C):**
- **X-axis**: Represents the overhead width in cm (ranging from 7 to 10).
- **Y-axis**: Represents the weight in kg (ranging from 100 to 300).
- The points are plotted to show the relationship between the widths and weights of the seals.
**Question:**
Find the linear correlation coefficient \( r \).
(Provide your answer rounded to three decimal places.)
---
Expert Solution
Correlation :
The linear correlation coefficient (r) measures the strength of relation between two variables and it's formula is stated as below
Where,
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