12 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 | 405.0 | 1567.0 | 1131.0 | 274.0 | 253.0 | 112.0 | 151.0 | 30.0 ||--------------|------|-------|--------|--------|-------|-------|-------|-------|------|| Justice Salary | 30 | 43 | 94 | 58 | 47 | 62 | 24 | 25 | 19 |**What are the null and alternative hypotheses?**- A. $ H_0: \rho \neq 0 $ $ H_1: \rho = 0 $- B. $ H_0: \rho = 0 $ $ H_1: \rho \neq 0 $- C. $ H_0: \rho = 0 $ $ H_1: \rho < 0 $- D. $ H_0: \rho = 0 $ $ H_1: \rho > 0 $**Construct a scatterplot. Choose the correct graph below.**The image presents four scatterplot options labeled A, B, C, and D. Each scatterplot plots Justice Salary (in thousands) against Court Income (in thousands).- **Graph A:** Displays various data points with no clear pattern, suggesting a lack of correlation.- **Graph B:** Shows a loosely linear pattern with a positive slope, hinting at a positive correlation.- **Graph C:** Displays a strong linear pattern with a positive slope, indicating a strong positive correlation.- **Graph D:** Similar to C, but with a slightly less distinct pattern, still indicating a positive correlation.*Note: Choose the graph that best represents the relationship between court income and justice salary based on the given data.**Click to select your answer(s).* 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.)Because the P-value is [dropdown] than the significance level 0.05, there [dropdown] sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of $\alpha = 0.05$.Based on the results, does it appear that justices might profit by levying larger fines?- A. It does not appear that justices might profit by levying larger fines.- B. It appears that justices profit the same despite the amount of the fines.- C. It does appear that justices might profit by issuing smaller fines.- D. It does appear that justices might profit by levying larger fines.

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Description: 12 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 =

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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 1 405.0|1567.이1131.이 274.0이 253.0 | 112.0 | 151.0 | 30.0 19 30 43 94 58 47 62 24 25 19 What are the null and alternative hypotheses? O A. Ho: p#0 O B. Ho: p=0 H,: p=0 H,: p#0 OC. Họ: p=0 O D. Ho: p=0 H,:p<0 H:p>0 Construct a scatterplot. Choose the correct graph below. OA. OB. OC. OD. AJustice Salary 100- AJustice Salary 100- Q AJustice Salary 100- AJustice Salary 1004 50- 50어 .. 50- 50- 0- 1600 0+ --- - 800 1600 0+ 800 800 1600 800 1600 Cut Inenma Cut IneAma Ct Inenma Cut incnma

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 1 405.0|1567.이1131.이 274.0이 253.0 | 112.0 | 151.0 | 30.0 19 30 43 94 58 47 62 24 25 19 What are the null and alternative hypotheses? O A. Ho: p#0 O B. Ho: p=0 H,: p=0 H,: p#0 OC. Họ: p=0 O D. Ho: p=0 H,:p<0 H:p>0 Construct a scatterplot. Choose the correct graph below. OA. OB. OC. OD. AJustice Salary 100- AJustice Salary 100- Q AJustice Salary 100- AJustice Salary 1004 50- 50어 .. 50- 50- 0- 1600 0+ --- - 800 1600 0+ 800 800 1600 800 1600 Cut Inenma Cut IneAma Ct Inenma Cut incnma

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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Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

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Question

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 | 405.0 | 1567.0 | 1131.0 | 274.0 | 253.0 | 112.0 | 151.0 | 30.0 |
|--------------|------|-------|--------|--------|-------|-------|-------|-------|------|
| Justice Salary | 30 | 43 | 94 | 58 | 47 | 62 | 24 | 25 | 19 |

**What are the null and alternative hypotheses?**

- A. $ H_0: \rho \neq 0 $
$ H_1: \rho = 0 $
- B. $ H_0: \rho = 0 $
$ H_1: \rho \neq 0 $
- C. $ H_0: \rho = 0 $
$ H_1: \rho < 0 $
- D. $ H_0: \rho = 0 $
$ H_1: \rho > 0 $

**Construct a scatterplot. Choose the correct graph below.**

The image presents four scatterplot options labeled A, B, C, and D. Each scatterplot plots Justice Salary (in thousands) against Court Income (in thousands).

- **Graph A:** Displays various data points with no clear pattern, suggesting a lack of correlation.
- **Graph B:** Shows a loosely linear pattern with a positive slope, hinting at a positive correlation.
- **Graph C:** Displays a strong linear pattern with a positive slope, indicating a strong positive correlation.
- **Graph D:** Similar to C, but with a slightly less distinct pattern, still indicating a positive correlation.

*Note: Choose the graph that best represents the relationship between court income and justice salary based on the given data.*

*Click to select your answer(s).*

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.)

Because the P-value is [dropdown] than the significance level 0.05, there [dropdown] sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of $\alpha = 0.05$.

Based on the results, does it appear that justices might profit by levying larger fines?

- A. It does not appear that justices might profit by levying larger fines.
- B. It appears that justices profit the same despite the amount of the fines.
- C. It does appear that justices might profit by issuing smaller fines.
- D. It does appear that justices might profit by levying larger fines.

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