**Title: Analysis of Court Income and Justice Salaries****Introduction:**Listed below are amounts of court income and salaries paid to town justices. All amounts are in thousands of dollars. Construct a scatterplot, find the value of the linear correlation coefficient $ r $, and determine 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?**Data:**| Court Income | 66.0 | 404.0 | 1567.0 | 1130.0 | 271.0 | 251.0 | 112.0 | 154.0 | 32.0 ||----------------|------|-------|--------|--------|-------|-------|-------|-------|------|| Justice Salary | 30 | 46 | 90 | 57 | 44 | 61 | 25 | 26 | 18 |**Hypotheses:**- **Null Hypothesis ( $ H_0 $ ):** $ \rho = 0 $- **Alternative Hypothesis ( $ H_1 $ ):** $ \rho \neq 0 $**Scatterplot Options:**The following scatterplots are provided as options to represent the relationship between Court Income and Justice Salary:- **Graph A:** Positively sloped data points correlating Justice Salary with Court Income.- **Graph B:** A more scattered distribution with no clear trend.- **Graph C:** A negatively sloped line indicating an inverse relationship.- **Graph D:** A random dispersion with no clear pattern.**Linear Correlation Analysis:**- **Linear Correlation Coefficient** $ r = \_\_\_ $. (Round to three decimal places as needed.)- **Test Statistic** $ t = \_\_\_ $. (Round to three decimal places as needed.)This analysis will aid in understanding whether the justice salaries are potentially influenced by the court income, potentially suggesting monetary incentives in decision making.

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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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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 incomes and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines? Court Income 66.0 402.0 1568.01131.0 270.0 250.0 1 12.0 150.0 32.0 D Justice Salary 29 46 90 58 45 61 24 25 18 What are the null and alternative hypotheses? O A. Ho: p=0 О В. Но: р30 Hiip0 O D. Ho: p+0 H1: p = 0
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 incomes and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines? Court Income Justice Salary 65.0 403.0 1568.01132.0 271.0 252.0 112.0 150.0 34.0 e 60 31 42 91 57 46 24 25 17 Ο Α. Η : ρ=0, B. Ho: p=0 H:p#0 H,:p>0 O C. Ho: p=0 O D. Ho: pz0 H1:p=0 H,:p<0 Construct a scatterplot. Choose the correct graph below. O A. OB. Oc. C. D. AJustice Salary 100- Q AJustice Salary 100- AJustice Salary 100- AJustice Salary 100- Q .. 50- 50- 50- . 50- 50- . 0- 0- 0- 800 1600 800 1600 800 1600 800 1600 Court Income Court Income Court Income Court Income The linear correlation coefficient is r= 0.869 (Round to three decimal…
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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 incomes and justice salaries? Based on the results, does it appear that justices might profit by levying larger fines? Court Income Justice Salary 65.0 406.0 1566.0 1131.0 274.0 253.0 110.0 152.0 31.0 e 29 45 94 58 46 61 25 26 19 The linear correlation coefficient is r= (Round to three decimal places as needed.) The test statistic is t=. (Round to three decimal places as needed.) The P-value is (Round to three decimal places as needed.) V than the significance level 0.05, there court incomes and justice salaries for a significance level of a = 0.05. Because the P-value is V sufficient evidence to support the claim that there is a linear correlation between Based…
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