2 ### Analysis of Court Income and Justice SalariesThe data provided below represents amounts of court income and salaries paid to town justices. All values are expressed in thousands of dollars. The objective is to construct a scatterplot, calculate the linear correlation coefficient \( r \), and determine the P-value using \( \alpha = 0.05 \). This analysis seeks to ascertain whether there is a significant linear relationship between court incomes and justice salaries, and if this might suggest a potential profit from levying larger fines.#### Data Table- **Court Income**: 66.0, 402.0, 1568.0, 1130.0, 274.0, 252.0, 112.0, 150.0, 34.0- **Justice Salary**: 29, 42, 94, 58, 44, 60, 26, 27, 17#### Hypotheses- **Null Hypothesis (\( H_0 \))**: \( \rho = 0 \)- **Alternative Hypotheses**: - A: \( \rho < 0 \) - B: \( \rho \neq 0 \) - C: \( \rho \neq 0 \) - D: \( \rho > 0 \)#### Scatterplot Options- **Graph A**: Displays a positive trend between court income and justice salary.- **Graph B**: Displays a negative trend between court income and justice salary.- **Graph C**: Displays a trend suggesting no clear relationship.- **Graph D**: Displays a positive trend with noticeable outliers.#### Statistical Analysis- **Linear Correlation Coefficient \( r \)**: _______ (Round to three decimal places)- **Test Statistic \( t \)**: _______ (Round to three decimal places)- **P-value**: _______ (Round to three decimal places)#### Conclusion- The P-value is _______ the significance level \( \alpha = 0.05 \). Thus, there is _______ evidence to support the claim of a linear correlation between court incomes and justice salaries. - **Based on the results, does it appear that justices might profit by levying larger fines?** - A: Yes, it does appear that justices might profit. - B: No, it does not appear that justices **Analysis of Court Income and Justice Salaries**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 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?**Data:**- **Court Income:** 66.0, 402.0, 1568.0, 1130.0, 274.0, 252.0, 112.0, 150.0, 34.0- **Justice Salary:** 29, 42, 94, 58, 44, 60, 26, 27, 17**Hypotheses:**- \( H_1: \rho < 0 \)- \( H_0: \rho \neq 0 \)- \( H_1: \rho = 0 \)- \( H_1: \rho \neq 0 \)- \( H_0: \rho = 0 \)- \( H_1: \rho > 0 \)*Construct a scatterplot. Choose the correct graph below:*- **Option A**- **Option B**- **Option C**- **Option D****Tasks:**1. Calculate the linear correlation coefficient \( r \). - (Round to three decimal places as needed)2. Compute the test statistic \( t \). - (Round to three decimal places as needed)3. Determine the P-value. - (Round to three decimal places as needed)**Conclusion:**Evaluate the P-value in relation to the significance level of 0.05 to determine if there is evidence of a linear correlation between court incomes and justice salaries. - \( \text{Because the P-value is } \__[?]\__ \text{ than the significance level of 0.05, there is \__[?]\__ sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries.} \)**Final Analysis:**Based on the results, does it appear that justices might profit by levying larger fines?- **A.**

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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 66.0 402.0 1568.01130.0 274.0 252 0 112.0 150.0 34.0 O 29 42 94 58 44 60 26 27 17 ..... What are the null and alternative hypotheses? O A. Ho p=0 H p<0 OC. Ho p#0 H p=0 O B. Ho p=0 H p#0 O D. Ho p=0 H, p>0 Construct a scatterplot. Choose the correct graph below. O A. OB. OC. OD. AJustice Salary 100- AJustice Salary Q AJustice Salary 100 Q AJustice Salary 100+ 100 - 50- 50+ EUET 50- 50- 50- 0++++- ++++ 800 Court Income 04 0++++++ +++++ 800 Court Income 1600 0+ 1600 Court Income 1600 800 1600 Court income ar The linear correlation coefficient is r= (Round to three decimal places as needed.) Is The test statistic is t= (Round to three decimal places as needed ) The P-value is (Round to three decimal places as needed ) Because the P-value is V than the significance level 0 05, there V 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?

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P