C. 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 linear 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 nonlinear correlation between the two variables. d.)  there is insufficient evidence to support the claim o

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C. 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 linear 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 nonlinear 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 reveals a distinct pattern that is not a straight-line 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 a straight-line pattern with positive slope.

d.) The scatterplot does not reveal a distinct pattern.

The image provides a dataset with two variables, \( x \) and \( y \), and instructions to complete parts (a) through (c) for correlation analysis, using a significance level of \( \alpha = 0.05 \).

### Dataset:
- \( x \): 10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5
- \( y \): 9.15, 8.14, 8.74, 8.76, 9.26, 8.11, 6.13, 3.11, 9.12, 7.26, 4.74

### Tasks:
1. **Construct a Scatterplot**: Choose the correct graph from options A, B, C, and D.
   - **Option A**: Displays points plotted with slight bends.
   - **Option B**: (Highlighted as correct) Shows a non-linear curved pattern resembling an inverted ‘U’ shape.
   - **Option C**: Displays a linear upward trend.
   - **Option D**: Exhibits a linear downward trend.

2. **Find the Linear Correlation Coefficient, \( r \)**:
   - Determine if there is sufficient evidence to support the claim of a linear correlation between \( x \) and \( y \).
   - Fill in the linear correlation coefficient \( r \) in the box provided and round to three decimal places.

The task involves evaluating the scatterplots and calculating the linear correlation coefficient to assess the relationship between the two variables.
Transcribed Image Text:The image provides a dataset with two variables, \( x \) and \( y \), and instructions to complete parts (a) through (c) for correlation analysis, using a significance level of \( \alpha = 0.05 \). ### Dataset: - \( x \): 10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5 - \( y \): 9.15, 8.14, 8.74, 8.76, 9.26, 8.11, 6.13, 3.11, 9.12, 7.26, 4.74 ### Tasks: 1. **Construct a Scatterplot**: Choose the correct graph from options A, B, C, and D. - **Option A**: Displays points plotted with slight bends. - **Option B**: (Highlighted as correct) Shows a non-linear curved pattern resembling an inverted ‘U’ shape. - **Option C**: Displays a linear upward trend. - **Option D**: Exhibits a linear downward trend. 2. **Find the Linear Correlation Coefficient, \( r \)**: - Determine if there is sufficient evidence to support the claim of a linear correlation between \( x \) and \( y \). - Fill in the linear correlation coefficient \( r \) in the box provided and round to three decimal places. The task involves evaluating the scatterplots and calculating the linear correlation coefficient to assess the relationship between the two variables.
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