Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between court incon and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines? Court Income Justice Salary 30 43 94 55 46 60 25 26 18 | 66.0 404.0 1568.01131.0 271.0 254.0O 1100 1530 320- H: p=0 Construct a scatterplot Choose the correct graph below. O A. OB. Oc. OD. Wustice Salany 100 Atice Salary 100 Justice Salary 100 Justice Salary 1004 50 50 50 p00 1600 B00 1600 s00 1600 1600 Court income Court income Court income Court income The linear correlation coefficient is r= 0.86 (Round to three decimal places as needed.) The test statistic is t= (Round to three decimal places as needed.) The Pvalue is 0 0027 (Round to three decimal places as needed.) Because the P-value is less than the significance level 0.05, there is sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of a = 0.05. Based on the results, does it appear that justices might profit by levying larger fines? O A. It does appear that justices might profit by levying larger fines. O B. It does not appear that justices might profit by levying larger fines. OC. It does appear that justices might profit by issuing smaller fines. O D. It appears that justices profit the same despite the amount of the fines.
Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between court incon and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines? Court Income Justice Salary 30 43 94 55 46 60 25 26 18 | 66.0 404.0 1568.01131.0 271.0 254.0O 1100 1530 320- H: p=0 Construct a scatterplot Choose the correct graph below. O A. OB. Oc. OD. Wustice Salany 100 Atice Salary 100 Justice Salary 100 Justice Salary 1004 50 50 50 p00 1600 B00 1600 s00 1600 1600 Court income Court income Court income Court income The linear correlation coefficient is r= 0.86 (Round to three decimal places as needed.) The test statistic is t= (Round to three decimal places as needed.) The Pvalue is 0 0027 (Round to three decimal places as needed.) Because the P-value is less than the significance level 0.05, there is sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of a = 0.05. Based on the results, does it appear that justices might profit by levying larger fines? O A. It does appear that justices might profit by levying larger fines. O B. It does not appear that justices might profit by levying larger fines. OC. It does appear that justices might profit by issuing smaller fines. O D. It appears that justices profit the same despite the amount of the fines.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Question
Transcribed Image Text:**Title: Analyzing Court Income and Justice Salaries**
Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear correlation coefficient \( r \), and find the P-value using \( \alpha = 0.05 \). Is there sufficient evidence to conclude that there is a linear correlation between court incomes and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines?
| Court Income | 660 | 404 | 1586 | 1131 | 771 | 540 | 1130 | 1534 | 320 |
|--------------------|-----|-----|------|------|-----|-----|------|------|-------|
| Justice Salary | 30 | 43 | 54 | 55 | 56 | 36 | 28 | 15 | 18 |
### Hypotheses:
- \( H_1: \rho < 0 \)
- \( H_1: \rho = 0 \)
### Construct a Scatterplot:
Choose the correct graph below.
- **Graph A:**
- **Scatter Placement**: Points are tightly clustered, indicating a likely correlation.
- **Axis Labels**: Court Income on X-axis and Justice Salary on Y-axis.
- **Graph B:**
- **Scatter Placement**: Points are loosely spread with no clear pattern.
- **Axis Labels**: Court Income on X-axis and Justice Salary on Y-axis.
- **Graph C:**
- **Scatter Placement**: Points show a downward trend.
- **Axis Labels**: Court Income on X-axis and Justice Salary on Y-axis.
- **Graph D:**
- **Scatter Placement**: Points somewhat evenly spaced horizontally.
- **Axis Labels**: Court Income on X-axis and Justice Salary on Y-axis.
**Correct choice: Graph C**
### Calculations:
1. **Linear Correlation Coefficient \( r \):**
- \( r = -0.86 \) (Round to three decimal places as needed.)
2. **Test Statistic \( t \):**
- Value to be determined and filled in provided space.
3. **P-value:**
- \( p = 0.0027 \) (Round
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