Homework Help is Here – Start Your Trial Now!
Math
Statistics
Use the given data set to complete parts. (a) through (c) below. (Use α = 0.05.) X y 10 9.14 O A. Ay 8 8.14 Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot. Choose the correct graph below. 10- 8- 6 4- 2- 0- 0 4 8 12 16 60000 13 8.73 Q E O B. Ay 10+ 84 9 8.76 6- 4- 2- 0+ 0 0000 88 4 8 12 16 Q Q 11 9.27 14 8.09 *** O C. A 6 6.13 10- 8- 6- 4- 2- 0- 0 4 8 12 16 Q 4 3.09 12 9.12 O D. Ay 10- 8- 6- 4 2- 0- 0 + Fut → . 4 8 b. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient is r= (Round to three decimal places as needed.) 7 7.26 12 16 Q Q 5 5 4.75 Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. E

Use the given data set to complete parts. (a) through (c) below. (Use α = 0.05.) X y 10 9.14 O A. Ay 8 8.14 Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot. Choose the correct graph below. 10- 8- 6 4- 2- 0- 0 4 8 12 16 60000 13 8.73 Q E O B. Ay 10+ 84 9 8.76 6- 4- 2- 0+ 0 0000 88 4 8 12 16 Q Q 11 9.27 14 8.09 *** O C. A 6 6.13 10- 8- 6- 4- 2- 0- 0 4 8 12 16 Q 4 3.09 12 9.12 O D. Ay 10- 8- 6- 4 2- 0- 0 + Fut → . 4 8 b. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient is r= (Round to three decimal places as needed.) 7 7.26 12 16 Q Q 5 5 4.75 Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below. E

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
### Correlation Analysis: A Step-by-Step Tutorial #### Data Set The given data set is as follows (Use α = 0.05): \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline x & 10 & 8 & 13 & 9 & 11 & 14 & 6 & 4 & 12 & 7 & 5 \\ \hline y & 9.14 & 8.14 & 8.73 & 8.76 & 9.27 & 8.09 & 6.13 & 3.09 & 9.12 & 7.26 & 4.75 \\ \hline \end{array} \] Click [here](#) to view a table of critical values for the correlation coefficient. #### Step-by-Step Instructions **a. Construct a Scatterplot** Choose the correct graph from the options below that represents the data set accurately: - **Option A:** ![Graph A](data:image/png;base64, ...) - This scatterplot shows a positive linear relationship between x and y. - **Option B:** ![Graph B](data:image/png;base64, ...) - This scatterplot displays a negative linear relationship between x and y. - **Option C:** ![Graph C](data:image/png;base64, ...) - This scatterplot indicates a positive but nonlinear relationship between x and y. - **Option D:** ![Graph D](data:image/png;base64, ...) - This scatterplot suggests a nonlinear relationship between x and y with possible curvature. **Correct Choice:** - [ ] A. - [ ] B. - [ ] C. - [ ] D. **b. Find the Linear Correlation Coefficient, \( r \)** Calculate the linear correlation coefficient using the given data and determine if there is sufficient evidence to support a claim of linear correlation between the variables. The formula to use is: \[ r = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{\sqrt{[n\sum{x^2} - (\sum{x})^2][n\sum{y^2} - (\sum{y})^2]}} \] - Round
Transcribed Image Text:### Correlation Analysis: A Step-by-Step Tutorial #### Data Set The given data set is as follows (Use α = 0.05): \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline x & 10 & 8 & 13 & 9 & 11 & 14 & 6 & 4 & 12 & 7 & 5 \\ \hline y & 9.14 & 8.14 & 8.73 & 8.76 & 9.27 & 8.09 & 6.13 & 3.09 & 9.12 & 7.26 & 4.75 \\ \hline \end{array} \] Click [here](#) to view a table of critical values for the correlation coefficient. #### Step-by-Step Instructions **a. Construct a Scatterplot** Choose the correct graph from the options below that represents the data set accurately: - **Option A:** ![Graph A](data:image/png;base64, ...) - This scatterplot shows a positive linear relationship between x and y. - **Option B:** ![Graph B](data:image/png;base64, ...) - This scatterplot displays a negative linear relationship between x and y. - **Option C:** ![Graph C](data:image/png;base64, ...) - This scatterplot indicates a positive but nonlinear relationship between x and y. - **Option D:** ![Graph D](data:image/png;base64, ...) - This scatterplot suggests a nonlinear relationship between x and y with possible curvature. **Correct Choice:** - [ ] A. - [ ] B. - [ ] C. - [ ] D. **b. Find the Linear Correlation Coefficient, \( r \)** Calculate the linear correlation coefficient using the given data and determine if there is sufficient evidence to support a claim of linear correlation between the variables. The formula to use is: \[ r = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{\sqrt{[n\sum{x^2} - (\sum{x})^2][n\sum{y^2} - (\sum{y})^2]}} \] - Round
**Educational Content: Table of Critical Values and Data Visualization** --- ### Table of Critical Values The table below provides critical values for statistical testing at significance levels of \(\alpha = 0.05\) and \(\alpha = 0.01\). This table is essential in determining whether to reject or fail to reject the null hypothesis in correlation tests. | \( n \) | \(\alpha = 0.05\) | \(\alpha = 0.01\) | |:--------:|:----------------:|:-----------------:| | 4 | 0.950 | 0.990 | | 5 | 0.878 | 0.959 | | 6 | 0.811 | 0.917 | | 7 | 0.754 | 0.875 | | 8 | 0.707 | 0.834 | | 9 | 0.666 | 0.798 | | 10 | 0.632 | 0.765 | | 11 | 0.602 | 0.735 | | 12 | 0.576 | 0.708 | | 13 | 0.553 | 0.684 | | 14 | 0.532 | 0.661 | | 15 | 0.514 | 0.641 | | 16 | 0.497 | 0.623 | | 17 | 0.482 | 0.606 | | 18 | 0.468 | 0.590 | | 19 | 0.456 | 0.575 | | 20 | 0.444 | 0.561 | | 21 | 0.433 | 0.549 | | 22 | 0.423 | 0.537 | | 23 | 0.413 | 0.526 | | 24 | 0.404 | 0.515 | | 25 | 0.396 | 0.505 | | 26 | 0.388
Transcribed Image Text:**Educational Content: Table of Critical Values and Data Visualization** --- ### Table of Critical Values The table below provides critical values for statistical testing at significance levels of \(\alpha = 0.05\) and \(\alpha = 0.01\). This table is essential in determining whether to reject or fail to reject the null hypothesis in correlation tests. | \( n \) | \(\alpha = 0.05\) | \(\alpha = 0.01\) | |:--------:|:----------------:|:-----------------:| | 4 | 0.950 | 0.990 | | 5 | 0.878 | 0.959 | | 6 | 0.811 | 0.917 | | 7 | 0.754 | 0.875 | | 8 | 0.707 | 0.834 | | 9 | 0.666 | 0.798 | | 10 | 0.632 | 0.765 | | 11 | 0.602 | 0.735 | | 12 | 0.576 | 0.708 | | 13 | 0.553 | 0.684 | | 14 | 0.532 | 0.661 | | 15 | 0.514 | 0.641 | | 16 | 0.497 | 0.623 | | 17 | 0.482 | 0.606 | | 18 | 0.468 | 0.590 | | 19 | 0.456 | 0.575 | | 20 | 0.444 | 0.561 | | 21 | 0.433 | 0.549 | | 22 | 0.423 | 0.537 | | 23 | 0.413 | 0.526 | | 24 | 0.404 | 0.515 | | 25 | 0.396 | 0.505 | | 26 | 0.388
Expert Solution
steps

Step by step

Solved in 5 steps with 7 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar 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
SEE MORE TEXTBOOKS