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nts SS rary ons 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 64.0 406.0 1567.0 1132.0 274.0 251.0 110.0 153.0 33.0 46 92 58 45 61 25 26 19 31 ... OA. Ho: p*0 OB. Hop=0 H₁: p<0 H₁: p=0 OC. Ho: p=0 H₁: p>0 D. Ho: p=0 H₁: p#0 Construct a scatterplot. Choose the correct graph below. OA. B. OD. AJustice Salary A Justice Salary Q AJustice Salary 100+ Q 100+ 100- 1. C O Ott 50 50- 50- n O 0 1600 800 1600 800 Court Income The linear correlation coefficient is r= (Round to three decimal places as needed.) 0- → D 0 800 1600 Court Income Q OC. 100+ 50 0 Court Income Q A Justice Salary 0 800 1600 Court Income

nts SS rary ons 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 64.0 406.0 1567.0 1132.0 274.0 251.0 110.0 153.0 33.0 46 92 58 45 61 25 26 19 31 ... OA. Ho: p*0 OB. Hop=0 H₁: p<0 H₁: p=0 OC. Ho: p=0 H₁: p>0 D. Ho: p=0 H₁: p#0 Construct a scatterplot. Choose the correct graph below. OA. B. OD. AJustice Salary A Justice Salary Q AJustice Salary 100+ Q 100+ 100- 1. C O Ott 50 50- 50- n O 0 1600 800 1600 800 Court Income The linear correlation coefficient is r= (Round to three decimal places as needed.) 0- → D 0 800 1600 Court Income Q OC. 100+ 50 0 Court Income Q A Justice Salary 0 800 1600 Court Income

MATLAB: An Introduction with Applications
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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Second part to this question is also what is test statistic t=
### Correlation Analysis between Court Income and Justice Salaries **Context:** This exercise aims to analyze the relationship between court income and the salaries paid to town justices. The data is provided in thousands of dollars. A scatterplot is constructed to visualize the data distribution, and the linear correlation coefficient \( r \) is calculated to assess the strength and direction of the relationship. The hypothesis testing at a significance level \( \alpha = 0.05 \) is conducted to evaluate if there is sufficient evidence of a linear correlation between court income and justice salaries. **Data Provided:** | Court Income (in thousands) | 64.0 | 406.0 | 1567.0 | 1132.0 | 274.0 | 251.0 | 110.0 | 153.0 | 33.0 | |-----------------------------|------|-------|--------|--------|-------|-------|-------|-------|------| | Justice Salary (in thousands) | 31 | 46 | 92 | 58 | 45 | 61 | 25 | 26 | 19 | **Hypotheses:** D. \( H_0: \rho = 0 \) (Null Hypothesis: No linear correlation) \( H_1: \rho \neq 0 \) (Alternative Hypothesis: Linear correlation exists) **Scatterplot Options:** From the provided options, select the correct scatter plot representing the given data. **Scatterplot Selection:** - **Option A:** Does not represent the correct data distribution. - **Option B:** Correct scatter plot selection based on visual analysis. - **Option C:** Does not represent the correct data distribution. - **Option D:** Does not represent the correct data distribution. **Correlation Coefficient Calculation:** The linear correlation coefficient \( r \) needs to be calculated and the value should be rounded to three decimal places. - **Formula:** \( r = \frac{\text{Cov}(X, Y)}{\sigma_X \sigma_Y} \) - Where \( \text{Cov}(X, Y) \) is the covariance between the variables X (Court Income) and Y (Justice Salary). - \( \sigma_X \) and \( \sigma_Y \) are the standard deviations of X and Y, respectively. **Note:** After calculation, the value of \( r \) should be filled in the blank. ### Conclusion:
Transcribed Image Text:### Correlation Analysis between Court Income and Justice Salaries **Context:** This exercise aims to analyze the relationship between court income and the salaries paid to town justices. The data is provided in thousands of dollars. A scatterplot is constructed to visualize the data distribution, and the linear correlation coefficient \( r \) is calculated to assess the strength and direction of the relationship. The hypothesis testing at a significance level \( \alpha = 0.05 \) is conducted to evaluate if there is sufficient evidence of a linear correlation between court income and justice salaries. **Data Provided:** | Court Income (in thousands) | 64.0 | 406.0 | 1567.0 | 1132.0 | 274.0 | 251.0 | 110.0 | 153.0 | 33.0 | |-----------------------------|------|-------|--------|--------|-------|-------|-------|-------|------| | Justice Salary (in thousands) | 31 | 46 | 92 | 58 | 45 | 61 | 25 | 26 | 19 | **Hypotheses:** D. \( H_0: \rho = 0 \) (Null Hypothesis: No linear correlation) \( H_1: \rho \neq 0 \) (Alternative Hypothesis: Linear correlation exists) **Scatterplot Options:** From the provided options, select the correct scatter plot representing the given data. **Scatterplot Selection:** - **Option A:** Does not represent the correct data distribution. - **Option B:** Correct scatter plot selection based on visual analysis. - **Option C:** Does not represent the correct data distribution. - **Option D:** Does not represent the correct data distribution. **Correlation Coefficient Calculation:** The linear correlation coefficient \( r \) needs to be calculated and the value should be rounded to three decimal places. - **Formula:** \( r = \frac{\text{Cov}(X, Y)}{\sigma_X \sigma_Y} \) - Where \( \text{Cov}(X, Y) \) is the covariance between the variables X (Court Income) and Y (Justice Salary). - \( \sigma_X \) and \( \sigma_Y \) are the standard deviations of X and Y, respectively. **Note:** After calculation, the value of \( r \) should be filled in the blank. ### Conclusion:
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