Answer:
Explanation:
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Full text:
Listed below are amounts of court income and salaries paid to the town justice. 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?
Court Income: 65.0, 402.0, 1567.0, 1132.0, 273.0, 251.0, 112.0, 156.0, 34.0
Justice Salary: 31, 46, 91, 56, 47, 60, 26, 27, 18
a. What are the null and alternative hypotheses?
To test if there is a linear correlation between the court income and the justice salary, you have to use the following hypotheses:
H₀: ρ = 0
H₁: ρ ≠ 0
b. Construct a scatterplot. See attachment.
c. The linear correlation coefficient r is: _____.
![r= \frac{sumX_1X_2-((sumX_1)(sumX_2))/(n) }{\sqrt{[sumX_1^2-((sumX_1)^2)/(n) ][sumX_2^2-((sumX_2)^2)/(n) ]} }](https://img.qammunity.org/2021/formulas/mathematics/college/vu5km70lsaj2icocgktb0qd0ew7fq4zvvv.png)
n= 9; ∑X₁= 3992; ∑X₁²= 4078308; ∑X₂= 409; ∑X₂²= 2232; ∑X₁X₂= 262123
r= 0.86
d. The P value is: _____.
This test is two-tailed and so is its p-value. I've calculated it using a statistics software:
p-value: 0.0027
e. Based on the results, does it appear that justices might profit by levying larger fines?
Using the p-value approach, the decision rule is:
If the p-value ≤ α, reject the null hypothesis.
If the p-value > α, do not reject the null hypothesis.
The calculated p-value is less than the significance level, then the decision is to reject the null hypothesis.
At a 5% significance level you can conclude that there is a linear correlation between the "court income" and the "Justice salary"
I hope this helps!