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Use the given data set to complete parts​ (a) through​ (c) below.​ (Use α=​0.05.)   x 10 8 13 9 11 14 6 4 12 7 5   y 9.14 8.15 8.74 8.78 9.25 8.09 6.12 3.09 9.13 7.27 4.75     View the table of critical values for the correlation coefficient. ( Table is attached)   a.  Construct a scatterplot. Choose the correct graph below.   ( Graphs are attached in picture)   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.)   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.   A. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. B. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables. C. There is sufficient evidence to support the claim of a linear correlation between the two variables. D. There is insufficient evidence to support the claim of a linear correlation between the two variables.   c. Identify the feature of the data that would be missed if part​ (b) was completed without constructing the scatterplot. Choose the correct answer below.   A. The scatterplot does not reveal a distinct pattern. B. The scatterplot reveals a distinct pattern that is a​ straight-line pattern with negative slope. C. The scatterplot reveals a distinct pattern that is not a​ straight-line pattern. D. The scatterplot reveals a distinct pattern that is a​ straight-line pattern with positive slope.

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use α=​0.05.)   x 10 8 13 9 11 14 6 4 12 7 5   y 9.14 8.15 8.74 8.78 9.25 8.09 6.12 3.09 9.13 7.27 4.75     View the table of critical values for the correlation coefficient. ( Table is attached)   a.  Construct a scatterplot. Choose the correct graph below.   ( Graphs are attached in picture)   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.)   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.   A. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. B. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables. C. There is sufficient evidence to support the claim of a linear correlation between the two variables. D. There is insufficient evidence to support the claim of a linear correlation between the two variables.   c. Identify the feature of the data that would be missed if part​ (b) was completed without constructing the scatterplot. Choose the correct answer below.   A. The scatterplot does not reveal a distinct pattern. B. The scatterplot reveals a distinct pattern that is a​ straight-line pattern with negative slope. C. The scatterplot reveals a distinct pattern that is not a​ straight-line pattern. D. The scatterplot reveals a distinct pattern that is a​ straight-line pattern with positive slope.

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
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Question #3

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use
α=​0.05.)
 
x
10
8
13
9
11
14
6
4
12
7
5
  
y
9.14
8.15
8.74
8.78
9.25
8.09
6.12
3.09
9.13
7.27
4.75
 
 
View the table of critical values for the correlation coefficient.
( Table is attached)
 
a.  Construct a scatterplot. Choose the correct graph below.
  ( Graphs are attached in picture)
 
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.)
 
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.
 
A. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables.
B. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables.
C. There is sufficient evidence to support the claim of a linear correlation between the two variables.
D. There is insufficient evidence to support the claim of a linear correlation between the two variables.
 
c. Identify the feature of the data that would be missed if part​ (b) was completed without constructing the scatterplot. Choose the correct answer below.
 
A. The scatterplot does not reveal a distinct pattern.
B. The scatterplot reveals a distinct pattern that is a​ straight-line pattern with negative slope.
C. The scatterplot reveals a distinct pattern that is not a​ straight-line pattern.
D. The scatterplot reveals a distinct pattern that is a​ straight-line pattern with positive slope.

 

a. Construct a scatterplot: Choose the correct graph below. **Graph A:** - This scatterplot shows a curve that first increases and then decreases. Points are plotted between approximately (2, 2) and (14, 6) with a peak around (8, 10). **Graph B:** - This scatterplot has a downward trend, where the data points form a straight line descending from left to right, starting around (0, 10) and ending at approximately (16, 0). **Graph C:** - This scatterplot displays a linear increase. The points are aligned in an upward diagonal, ranging from around (0, 0) to (16, 10). **Graph D:** - This scatterplot illustrates an upward trend with points that are less tightly clustered compared to Graph C, starting near (2, 4) and ascending towards (14, 8). Each graph depicts a different trend, illustrating various possible relationships between the variables, which are not labeled here but could represent any dataset where scatterplots are useful for visualizing data distribution and trends.
Transcribed Image Text:a. Construct a scatterplot: Choose the correct graph below. **Graph A:** - This scatterplot shows a curve that first increases and then decreases. Points are plotted between approximately (2, 2) and (14, 6) with a peak around (8, 10). **Graph B:** - This scatterplot has a downward trend, where the data points form a straight line descending from left to right, starting around (0, 10) and ending at approximately (16, 0). **Graph C:** - This scatterplot displays a linear increase. The points are aligned in an upward diagonal, ranging from around (0, 0) to (16, 10). **Graph D:** - This scatterplot illustrates an upward trend with points that are less tightly clustered compared to Graph C, starting near (2, 4) and ascending towards (14, 8). Each graph depicts a different trend, illustrating various possible relationships between the variables, which are not labeled here but could represent any dataset where scatterplots are useful for visualizing data distribution and trends.
This table shows the critical values for testing the null hypothesis (\( H_0: \rho = 0 \)) against the alternative hypothesis (\( H_a: \rho \neq 0 \)) based on different sample sizes (\( n \)) and significance levels (\( \alpha \)) of .05 and .01. The values provided help decide whether to reject the null hypothesis. ### Table of Critical Values | \( n \) | \(\alpha = .05\) | \(\alpha = .01\) | |---------|-----------------|-----------------| | 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 | | 25 | 0.396 | 0.505 | | 30 | 0.361 | 0.463 | | 35 | 0.335 | 0.430 | | 40 | 0.312 | 0.402 | | 45 | 0.294 | 0.378 | | 50 | 0.279
Transcribed Image Text:This table shows the critical values for testing the null hypothesis (\( H_0: \rho = 0 \)) against the alternative hypothesis (\( H_a: \rho \neq 0 \)) based on different sample sizes (\( n \)) and significance levels (\( \alpha \)) of .05 and .01. The values provided help decide whether to reject the null hypothesis. ### Table of Critical Values | \( n \) | \(\alpha = .05\) | \(\alpha = .01\) | |---------|-----------------|-----------------| | 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 | | 25 | 0.396 | 0.505 | | 30 | 0.361 | 0.463 | | 35 | 0.335 | 0.430 | | 40 | 0.312 | 0.402 | | 45 | 0.294 | 0.378 | | 50 | 0.279
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