**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

The investigator is interested to test whether there is linear correlation between court income and Justice salary. EXCEL software can be used to draw a scatterplot for the given data. Software Procedure: The step-by-step procedure to draw a scatterplot using EXCEL software is given below: Open an EXCEL file. Enter the data of the variable Court Income in column A and name it as Court Income. Enter the data of the variable Justice Salary in column B and name it as Justice Salary. Select Data and go to Insert tab. Select All charts > Scatterplot. Click OK. The scatterplot is shown below: By comparing the obtained scatterplot and the given scatterplots, the obtained scatterplot matches with the scatterplot in Option(A). Therefore, the correct answer is Option(A).Correlation coefficient: Correlation can be calculated using EXCEL software: In any cell, enter the formula "CORREL(A2:A10,B2:B10)”, the correlation coefficient between the variables court income and Justice salary is r = 0.8687. The linear correlation coefficient r is 0.8687. Significance test: In order to test the hypothesis regarding the relation between a paired set of n observations (xi, yi), a significance test for correlation is appropriate. Thus, the sampling distribution used in the given scenario is “Student’s t with n – 2 degrees of freedom”. Denote r as the sample correlation coefficient between court income and Justice salary. Denote ρ as the population correlation coefficient between court income and Justice salary. The null and alternate hypotheses are stated below: Null hypothesis H0: H0: ρ = 0 That is, there exist no linear relationship between the variable’s court income and Justice salary. H1: ρ ≠ 0 That is, there exist linear relationship between the variable’s court income and Justice salary.Test statistic: The sample test statistic is obtained from the calculations given below: t=rn-21-r2=0.86879-21-0.86872=2.29840.4953=4.640df=n-2=9-2=7 Obtain the P - value: The degrees of freedom is d.f = 7. The step by step procedure to obtain the P - value is given below: Step 1: Open an EXCEL sheet. Step 2: In any cell type the formula “=2*(1-T.DIST.2T(4.64,7,TRUE)). Step 3: Click on Enter. Therefore, the P-value is obtained as 0.0024. Decision rule: The level of significance is α = 0.05. Decision rule based on P-value approach: If P-value ≤ α, then reject the null hypothesis H0. If P-value > α, then fail to reject the null hypothesis H0. Conclusion based on P-value approach: The P-value is 0.0024 and α value is 0.05. Here, P-value is less than the value. That is, 0.0024 (=P-value) < 0.05 (=α). By the rejection rule, reject the null hypothesis H0. Therefore, there exist linear relationship between the variable’s court income and Justice salary. 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 α = 0.05. Since, the correlation is positive, it can be concluded that the justice salary increases with the increase in court income. Therefore, Option(A) is correct.