Listed below are amounts of court income and salaries paid to the town justices.
ID: 3331549 • Letter: L
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
alphaequals=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
405.0405.0
1566.01566.0
1131.01131.0
271.0271.0
253.0253.0
112.0112.0
155.0155.0
31.031.0
Justice Salary
3131
4545
9090
5555
4545
6161
2626
2727
1818
What are the null and alternative hypotheses?
A.
Upper H 0H0:
rhoequals=0
Upper H 1H1:
rhonot equals0
Your answer is correct.
B.
Upper H 0H0:
rhoequals=0
Upper H 1H1:
rholess than<0
C.
Upper H 0H0:
rhonot equals0
Upper H 1H1:
rhoequals=0
D.
Upper H 0H0:
rhoequals=0
Upper H 1H1:
rhogreater than>0
Construct a scatterplot. Choose the correct graph below.
A.
08001600050100Court IncomeJustice Salary
Edit Coordinates... (0,0)
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).
B.
08001600050100Court IncomeJustice Salary
Edit Coordinates... (0,0)
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, 18); (60, 32); (120, 26); (160, 28); (260, 62); (280, 46); (400, 46); (1140, 56); (1560, 90).Your answer is correct.
C.
08001600050100Court IncomeJustice Salary
Edit Coordinates... (0,0)
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).
D.
08001600050100Court IncomeJustice Salary
Edit Coordinates... (0,0)
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).The linear correlation coefficient r is
0.858 0.858.
(Round to three decimal places as needed.)
The test statistic t is
4.419 4.419.
(Round to three decimal places as needed.)
The P-value is
nothing .
(Round to three decimal places as needed.)
Court Income
66.066.0
405.0405.0
1566.01566.0
1131.01131.0
271.0271.0
253.0253.0
112.0112.0
155.0155.0
31.031.0
Open in StatCrunch + Copy to Clipboard + Open in Excel +Justice Salary
3131
4545
9090
5555
4545
6161
2626
2727
1818
Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: Justice Salary
Independent Variable: Court Income
Justice Salary = 28.408888 + 0.035669175 Court Income
Sample size: 9
R (correlation coefficient) = 0.85797812
R-sq = 0.73612646
Estimate of error standard deviation: 12.257258
Parameter estimates:
Analysis of variance table for regression model:
Hence,
P - value = 0.003
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 28.408888 5.4312752 0 7 5.230611 0.0012 Slope 0.035669175 0.0080717139 0 7 4.4190337 0.0031Related Questions
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