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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 α=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?

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 α=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?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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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 α=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?

 

# Understanding P-Values and Hypothesis Testing ### The P-value is [ ]. *(Round to three decimal places as needed.)* ### Explanation: - The P-value is compared to the significance level (α = 0.05) to determine whether there is sufficient evidence to support the claim of a linear correlation between court incomes and justice salaries. ### Decision Rule: - **If the P-value is less than the significance level of 0.05**, there is sufficient evidence to support the claim. - **If the P-value is greater than the significance level of 0.05**, there is not sufficient evidence to support the claim. ### Question: Based on the results, does it appear that justices might profit by levying larger fines? ### Options: - **A.** It appears that justices profit the same despite the amount of the fines. - **B.** It does appear that justices might profit by issuing smaller fines. - **C.** It does not appear that justices might profit by levying larger fines. - **D.** It does appear that justices might profit by levying larger fines. ### Evaluation: Select the appropriate option based on the comparison of the P-value with the significance level. *Note: Ensure to enter the correct P-value rounded to three decimal places in the designated field before proceeding with the analysis.*
Transcribed Image Text:# Understanding P-Values and Hypothesis Testing ### The P-value is [ ]. *(Round to three decimal places as needed.)* ### Explanation: - The P-value is compared to the significance level (α = 0.05) to determine whether there is sufficient evidence to support the claim of a linear correlation between court incomes and justice salaries. ### Decision Rule: - **If the P-value is less than the significance level of 0.05**, there is sufficient evidence to support the claim. - **If the P-value is greater than the significance level of 0.05**, there is not sufficient evidence to support the claim. ### Question: Based on the results, does it appear that justices might profit by levying larger fines? ### Options: - **A.** It appears that justices profit the same despite the amount of the fines. - **B.** It does appear that justices might profit by issuing smaller fines. - **C.** It does not appear that justices might profit by levying larger fines. - **D.** It does appear that justices might profit by levying larger fines. ### Evaluation: Select the appropriate option based on the comparison of the P-value with the significance level. *Note: Ensure to enter the correct P-value rounded to three decimal places in the designated field before proceeding with the analysis.*
**Title: Analysis of Correlation Between Court Income and Justice Salaries** **Text:** 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 | 66.0 | 403.0 | 1567.0 | 1131.0 | 272.0 | 254.0 | 112.0 | 156.0 | 33.0 | |--------------|------|-------|--------|--------|-------|-------|-------|-------|-------| | Justice Salary | 30 | 45 | 92 | 56 | 45 | 61 | 25 | 26 | 18 | **What are the null and alternative hypotheses?** - A. \( H_0: \rho = 0 \) \( H_1: \rho > 0 \) - B. \( H_0: \rho = 0 \) \( H_1: \rho \neq 0 \) - C. \( H_0: \rho \neq 0 \) \( H_1: \rho = 0 \) - D. \( H_0: \rho = 0 \) \( H_1: \rho < 0 \) **Construct a scatterplot. Choose the correct graph below.** - **Option A:** - Depicts scattered points suggesting a weak positive relationship between court income and justice salary. - **Option B:** - Points show some clustering with a visible positive trend. - **Option C:** - Displays scattered points without a clear pattern, suggesting no strong relationship. - **Option D:** - Shows points scattered with a potential weak positive trend. **The linear correlation coefficient is \( r = \) \_\_\_.** *(Round to three decimal places as needed.)* **The test statistic is \( t = \) \_\_\_.** *(Round to three decimal
Transcribed Image Text:**Title: Analysis of Correlation Between Court Income and Justice Salaries** **Text:** 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 | 66.0 | 403.0 | 1567.0 | 1131.0 | 272.0 | 254.0 | 112.0 | 156.0 | 33.0 | |--------------|------|-------|--------|--------|-------|-------|-------|-------|-------| | Justice Salary | 30 | 45 | 92 | 56 | 45 | 61 | 25 | 26 | 18 | **What are the null and alternative hypotheses?** - A. \( H_0: \rho = 0 \) \( H_1: \rho > 0 \) - B. \( H_0: \rho = 0 \) \( H_1: \rho \neq 0 \) - C. \( H_0: \rho \neq 0 \) \( H_1: \rho = 0 \) - D. \( H_0: \rho = 0 \) \( H_1: \rho < 0 \) **Construct a scatterplot. Choose the correct graph below.** - **Option A:** - Depicts scattered points suggesting a weak positive relationship between court income and justice salary. - **Option B:** - Points show some clustering with a visible positive trend. - **Option C:** - Displays scattered points without a clear pattern, suggesting no strong relationship. - **Option D:** - Shows points scattered with a potential weak positive trend. **The linear correlation coefficient is \( r = \) \_\_\_.** *(Round to three decimal places as needed.)* **The test statistic is \( t = \) \_\_\_.** *(Round to three decimal
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