Question

Listed below are amount of court income and salaries paid to the town justices. All amounts are in the thousands of dollars. Construct a scatteplot salaries? Base on the results, dose it appears that justices might profit by levying large fines?
Court Income- 66.0 405.0 1566.0 1130.0 273.0
Just Salary-         31   43         90        57      48

250.0 110.0 150.0 31.0
62          26     27   17
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Answer 1

I have used excel to construct scatter plot and R code to find the linear correlation coefficient and to test for significance of correlation coefficient between the two variables.

SCATTER PLOT:

From the scatter plot, both the variables "court time" and "justice salary" move in the same positive direction. In other words, as one variable increases, the other variable also increases. Since there is a uphill straight (linear) pattern, there is a positive, linear association between the two variables "court time" and "justice salary".

LINEAR CORRELATION COEFFICIENT:

The Pearson correlation coefficient between "court time" and "justice salary" is . Since the sign of the correlation coefficient is positive and it is close to 1, there is a strong uphill (positive) linear relationship between the variables "court time" and "justice salary".

TEST FOR SIGNIFICANCE OF CORRELATION COEFFICIENT:

HYPOTHESIS:

The hypothesis is given by,

(That is, there is no statistically significant linear relationship (correlation) between court time and justice salary.)

(That is, there is statistically significant linear relationship (correlation) between court time and justice salary.)

LEVEL OF SIGNIFICANCE: .

R OUTPUT FOR TEST OF SIGNIFICANCE OF CORRELATION COEFFICIENT:

From the above output, the p value of correlation coefficient is . Since the p value is less than the significance level , we reject the null hypothesis and conclude that there is statistically significant linear relationship (correlation) between the variables court time and justice salary. In other words, there is sufficient evidence to conclude that there is statistically significant linear relationship (correlation) between the variables court time and justice salary. Thus justices might profit by levying large fines.