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pantera1 [17]
3 years ago
13

Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Constr

uct 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 g

Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
6 0

Answer:

Step-by-step explanation:

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>

r= \frac{sumX_1X_2-\frac{(sumX_1)(sumX_2)}{n} }{\sqrt{[sumX_1^2-\frac{(sumX_1)^2}{n} ][sumX_2^2-\frac{(sumX_2)^2}{n} ]} }

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!

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