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.

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 alpha equals0.05 . 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 64.0 405.0 1567.0 1132.0...

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 alpha equals0.05 . 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 64.0 402.0 1568.0 1130.0...

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 alphaα=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?
Court Income
65.0
406.0
1567.0
1132.0
272.0
253.0...

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
alpha
equals0.05
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 Justice_Salary
65.0 30
402.0 43
1568.0 ...

Listed below are amounts of court income and salaries paid to
the town justices. all amounts are in thousands of dollars.
Court income 66.0 403.0 1566.0 113.0 270.0 253.0 110.0 156.0
34.0
justice salary 29 46 90 57 44 62 26 27 17
the percent of variations in justice salary that can be
explained by court income is, approximately = _ (answer with a
percent rounded to the hundreths decimal place)

Listed below are amounts of court income and salaries paid to
the town justices for a certain town. All amounts are in thousands
of dollars. Find the (a) explained variation, (b) unexplained
variation, and (c) indicated prediction interval. There is
sufficient evidence to support a claim of a linear correlation, so
it is reasonable to use the regression equation when making
predictions. For the prediction interval, use a 99% confidence
level with a court income of $800,000.
Court_Income Justice_Salary
62...

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