Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from women, and the four points in the upper right corner are from men. Complete parts (a) through (e) below. :: 3 6 9 12
Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from women, and the four points in the upper right corner are from men. Complete parts (a) through (e) below. :: 3 6 9 12
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter9: Solving Quadratic Functions
Section: Chapter Questions
Problem 4CA
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Question
![**Question:**
Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from women, and the four points in the upper right corner are from men. Complete parts (a) through (e) below.
*Include scatterplot image*
**Scatterplot Explanation:**
The scatterplot consists of two distinct clusters of points:
- **Lower Left Corner:** It has a group of four points concentrated around the coordinates ([0,3], [0,6], [3,3], [3,6]).
- **Upper Right Corner:** It has another group of four points concentrated around the coordinates ([9,9], [9,12], [12,9], [12,12]).
**Tasks:**
(a) The correlation coefficient for the points in the lower left corner is \( r = \) ____.
(Type an integer or a fraction.)
(b) Do the four points in the upper right corner have the same correlation coefficient?
- A. No, because the four points in the upper right corner form the same pattern as the four points in the lower left corner.
- B. Yes, because the four points in the upper right corner form the same pattern as the four points in the lower left corner.
- C. Yes, because the four points in the upper right corner form a different pattern from the four points in the lower left corner.
- D. No, because the four points in the upper right corner form a different pattern from the four points in the lower left corner.
(c) Find the value of the linear correlation coefficient using all eight points. What does that value suggest about the relationship between \( x \) and \( y \)? Use \( \alpha = 0.05 \).
The correlation coefficient for all eight points is \( r = \) ____.
(Round to three decimal places as needed.)
(d) Using \( \alpha = 0.05 \), what does \( r \) suggest about the relationship between \( x \) and \( y \)?
- A. There is sufficient evidence to support the claim of a linear correlation because the correlation coefficient is greater than the critical value.
- B. There is sufficient evidence to support the claim of a linear correlation because the correlation coefficient is less than the critical value.
- C. There is not sufficient evidence to support the claim of a linear correlation because the correlation coefficient is less than the critical value.
- D. There is not sufficient evidence to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cc7f00e-28f4-4f9d-9775-3cbc7937b5d3%2Ffabdf106-90bf-4a70-91f7-5b24db53f148%2Fhqfr3vl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Refer to the accompanying scatterplot. The four points in the lower left corner are measurements from women, and the four points in the upper right corner are from men. Complete parts (a) through (e) below.
*Include scatterplot image*
**Scatterplot Explanation:**
The scatterplot consists of two distinct clusters of points:
- **Lower Left Corner:** It has a group of four points concentrated around the coordinates ([0,3], [0,6], [3,3], [3,6]).
- **Upper Right Corner:** It has another group of four points concentrated around the coordinates ([9,9], [9,12], [12,9], [12,12]).
**Tasks:**
(a) The correlation coefficient for the points in the lower left corner is \( r = \) ____.
(Type an integer or a fraction.)
(b) Do the four points in the upper right corner have the same correlation coefficient?
- A. No, because the four points in the upper right corner form the same pattern as the four points in the lower left corner.
- B. Yes, because the four points in the upper right corner form the same pattern as the four points in the lower left corner.
- C. Yes, because the four points in the upper right corner form a different pattern from the four points in the lower left corner.
- D. No, because the four points in the upper right corner form a different pattern from the four points in the lower left corner.
(c) Find the value of the linear correlation coefficient using all eight points. What does that value suggest about the relationship between \( x \) and \( y \)? Use \( \alpha = 0.05 \).
The correlation coefficient for all eight points is \( r = \) ____.
(Round to three decimal places as needed.)
(d) Using \( \alpha = 0.05 \), what does \( r \) suggest about the relationship between \( x \) and \( y \)?
- A. There is sufficient evidence to support the claim of a linear correlation because the correlation coefficient is greater than the critical value.
- B. There is sufficient evidence to support the claim of a linear correlation because the correlation coefficient is less than the critical value.
- C. There is not sufficient evidence to support the claim of a linear correlation because the correlation coefficient is less than the critical value.
- D. There is not sufficient evidence to
![### Analysis of Scatterplot Data
#### Scatterplot Overview
The scatterplot presents data points that represent measurements from men and women, divided as follows:
- **Lower Left Corner**: Represents measurements from women.
- **Upper Right Corner**: Represents measurements from men.
Each set of points is to be analyzed for potential linear correlations.
#### Question (a)
**Examine the pattern of the four points in the lower left corner (from women) and subjectively determine whether there appears to be a correlation between x and y for women. Choose the correct answer below.**
1. **A.** There appears to be a linear correlation because the points form a line.
2. **B.** There appears to be a linear correlation because the points form an obvious pattern.
3. **C.** There does not appear to be a linear correlation because the points do not form a line.
4. **D.** There does not appear to be a linear correlation because the points form an obvious pattern.
#### Question (b)
**Examine the pattern of the four points in the upper right corner (from men) and subjectively determine whether there appears to be a correlation between x and y for men. Choose the correct answer below.**
1. **A.** There appears to be a linear correlation because the points form an obvious pattern.
2. **B.** There appears to be a linear correlation because the points form a line.
3. **C.** There does not appear to be a linear correlation because the points form an obvious pattern.
4. **D.** There does not appear to be a linear correlation because the points do not form a line.
#### Question (c)
**Find the linear correlation coefficient using only the four points in the lower left corner (for women). Will the four points in the upper right corner (for men) have the same linear correlation coefficient?**
Provide the correlation coefficient for the points in the lower left corner:
\[ \text{The correlation coefficient for the points in the lower left corner is } r = \boxed{} \]
Given these questions and the provided scatterplot, the analysis should focus on identifying subjective patterns to assess correlation and calculating the correlation coefficient.
#### Graph Explanation
The scatterplot features:
- An x-axis labeled from 0 to 12.
- A y-axis labeled from 0 to 12.
- Two distinct clusters of points:
- The lower left corner (cluster for women) includes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cc7f00e-28f4-4f9d-9775-3cbc7937b5d3%2Ffabdf106-90bf-4a70-91f7-5b24db53f148%2F3eo6yu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analysis of Scatterplot Data
#### Scatterplot Overview
The scatterplot presents data points that represent measurements from men and women, divided as follows:
- **Lower Left Corner**: Represents measurements from women.
- **Upper Right Corner**: Represents measurements from men.
Each set of points is to be analyzed for potential linear correlations.
#### Question (a)
**Examine the pattern of the four points in the lower left corner (from women) and subjectively determine whether there appears to be a correlation between x and y for women. Choose the correct answer below.**
1. **A.** There appears to be a linear correlation because the points form a line.
2. **B.** There appears to be a linear correlation because the points form an obvious pattern.
3. **C.** There does not appear to be a linear correlation because the points do not form a line.
4. **D.** There does not appear to be a linear correlation because the points form an obvious pattern.
#### Question (b)
**Examine the pattern of the four points in the upper right corner (from men) and subjectively determine whether there appears to be a correlation between x and y for men. Choose the correct answer below.**
1. **A.** There appears to be a linear correlation because the points form an obvious pattern.
2. **B.** There appears to be a linear correlation because the points form a line.
3. **C.** There does not appear to be a linear correlation because the points form an obvious pattern.
4. **D.** There does not appear to be a linear correlation because the points do not form a line.
#### Question (c)
**Find the linear correlation coefficient using only the four points in the lower left corner (for women). Will the four points in the upper right corner (for men) have the same linear correlation coefficient?**
Provide the correlation coefficient for the points in the lower left corner:
\[ \text{The correlation coefficient for the points in the lower left corner is } r = \boxed{} \]
Given these questions and the provided scatterplot, the analysis should focus on identifying subjective patterns to assess correlation and calculating the correlation coefficient.
#### Graph Explanation
The scatterplot features:
- An x-axis labeled from 0 to 12.
- A y-axis labeled from 0 to 12.
- Two distinct clusters of points:
- The lower left corner (cluster for women) includes
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