Which property justifies this statement?
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Hello!
<em>Full text:</em>
<em>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? </em>
<em> Court Income: 65.0, 402.0, 1567.0, 1132.0, 273.0, 251.0, 112.0, 156.0, 34.0 </em>
<em> Justice Salary: 31, 46, 91, 56, 47, 60, 26, 27, 18 </em>
<em>a. What are the null and alternative hypotheses? </em>
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
<em>b. Construct a scatterplot. </em>See attachment.
<em>c. The linear correlation coefficient r is: _____. </em>
n= 9; ∑X₁= 3992; ∑X₁²= 4078308; ∑X₂= 409; ∑X₂²= 2232; ∑X₁X₂= 262123
r= 0.86
<em>d. The P value is: _____. </em>
This test is two-tailed and so is its p-value. I've calculated it using a statistics software:
p-value: 0.0027
<em>e. Based on the results, does it appear that justices might profit by levying larger fines?</em>
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!
