Listed below are amounts of court income and salaries paid to the town justices.

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 =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?

a. the linear correlation coefficient r is ?? (round to three decimal places as needed)

b. the test statisitc t is ?? ( round to three decmial places as needed)

c. The p value is ?? (round to three decimal places as needed)

d. Because the p value is ?? than the significance level 0.05, there ?? sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of =0.05.

e. based on the results, does it appear that justices might profit by levying larger fines?

(a). it does appear that justices might profit by issuing smaller fines

(b). it appears that justices profit the same despite the amount of the fines

(c). it does appear that justices might profit by levying larger fines

(d). it does not appear that justies might profit by levying larger fines

court income 66.0 404.0 1566.0 1132.0 272.0 250.0 111.0 152.0 32.0 Justice Salary 31 43 91 55 48 62 26 27 18

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Justice Salary
Independent Variable: Court Income
Justice Salary = 28.692473 + 0.035826285 Court Income
Sample size: 9
R (correlation coefficient) = 0.84764523
R-sq = 0.71850244
Estimate of error standard deviation: 12.881446

Parameter estimates:

Analysis of variance table for regression model:

Hence,

a) r = 0.848

b) t = 4.227

c) p value = 0.004

d) Less; is

e) It does appear that justices might profit by levying larger fines. Option C is correct.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 28.692473 5.7026983 0 7 5.0313853 0.0015 Slope 0.035826285 0.0084757073 0 7 4.2269375 0.0039

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