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

equals0.05

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
65.0   30
402.0   43
1568.0   93
1131.0   58
273.0   46
254.0   62
111.0   26
154.0   27
30.0   17

What are the null and alternative​ hypotheses?

Answer 1

65	30
402	43
1568	93
1131	58
273	46
254	62
111	26
154	27
30	17

The Scatterplot using Excel is

The Value of linear correlation coefficient using Excel Command is, "=correl(x,y)"

where x is "Court Income" And y is "Justice Salary"

We get, r=correlation= 0.8703

The Null Hypothesis is

H₀: There is no correlation between court incomes and justice salaries

Versus

H_a: There is correlation between court incomes and justice salaries

So therefore the p value corresponding to r=0.8703 using Pearsons table is 0.024

p-value=0.024

Here, a=level of significance = 0.05 - Given

so therefore, p-value<a

so therefore we fail to accept H₀.

Conclusion: There is Sufficient evidence to conclude that there is linear correlation between court incomes and justice salaries.

That is, It Appear that Justice might profit by levying larger fines.