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 alphaαequals=0.050.05. 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
66.066.0
403.0403.0
1566.01566.0
1130.01130.0
272.0272.0
253.0253.0
111.0111.0
153.0153.0
33.033.0

Justice Salary
2929
4646
9292
5656
4545
6060
2424
2525
1919
What are the null and alternative​ hypotheses?
A.
Upper H 0H0​: rhoρnot equals≠0
Upper H 1H1​: rhoρequals=0
B.
Upper H 0H0​: rhoρequals=0
Upper H 1H1​: rhoρnot equals≠0
C.
Upper H 0H0​: rhoρequals=0
Upper H 1H1​: rhoρless than<0
D.
Upper H 0H0​: rhoρequals=0
Upper H 1H1​: rhoρgreater than>0
Construct a scatterplot. Choose the correct graph below.
A.
0
800
1600
0
50
100
Court Income
Justice Salary

A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (220, 84); (220, 80); (360, 80); (400, 70); (580, 84); (740, 58); (1080, 62); (1120, 30); (1420, 44).
B.
0
800
1600
0
50
100
Court Income
Justice Salary

A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (260, 84); (420, 24); (640, 56); (760, 86); (880, 48); (900, 34); (1040, 86); (1260, 46); (1480, 18).
C.
0
800
1600
0
50
100
Court Income
Justice Salary

A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (40, 20); (60, 30); (120, 24); (160, 26); (260, 60); (280, 46); (400, 46); (1140, 56); (1560, 92).
D.
0
800
1600
0
50
100
Court Income
Justice Salary

A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (140, 14); (140, 36); (340, 42); (660, 54); (740, 66); (900, 74); (1280, 90); (1320, 14); (1420, 74).
The linear correlation coefficient r is
nothing.
​(Round to three decimal places as​ needed.)
The test statistic t is
nothing.
​(Round to three decimal places as​ needed.)
The​ P-value is
nothing.
​(Round to three decimal places as​ needed.)
Because the​ P-value is
▼
less
greater
than the significance level 0.050.05​, there
▼
is not
is
sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of alphaαequals=0.050.05.
Based on the​ results, does it appear that justices might profit by levying larger​ fines?
A.
It does appear that justices might profit by levying larger fines.
B.
It does appear that justices might profit by issuing smaller fines.
C.
It does not appear that justices might profit by levying larger fines.
D.
It appears that justices profit the same despite the amount of the fines.

Answer 1

Because the​ P-value is less than the significance level 0.05​, there is sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of α=0.05.

Option A. It does appear that justices might profit by levying larger fines.