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 alphaequals0.05. 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?


b. Construct a scatterplot.


c. The linear correlation coefficient r is: _____.


d. The P value is: _____.

Answer 1

H0 : β = 0

H1 : β = 0

R = 0.8642

P value = 0.002654

Step-by-step explanation:

Null hypothesis : H0 : β = 0

Alternative hypothesis : H1 : β ≠ 0

The correlation Coefficient, R value as obtained using a correlation Coefficient calculator is 0.8642. This depicts that a strong positive relationship exists between court income and Justice salary.

The Pvalue using the Pvalue calculator (R = 0.8642, N = 9) = 0.002654

The Pvalue < α

0.002654< 0.05 ; Hence, we reject H0.