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=0.05.

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
64.0   31
404.0   45
1566.0   93
1131.0   55
270.0   46
253.0   60
112.0   26
150.0   27
30.0   19

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​:

rhoρgreater than>0

C.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρnot equals≠0

D.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρless than<0

Construct a scatterplot. Choose the correct graph below.

A.

08001600050100Court IncomeJustice 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).

B.

08001600050100Court IncomeJustice 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, 32); (120, 26); (160, 28); (260, 60); (280, 46); (400, 46); (1140, 56); (1560, 94).

C.

08001600050100Court IncomeJustice 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).

D.

08001600050100Court IncomeJustice 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).

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 not appear that justices might profit by levying larger fines.

B.

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

C.

It appears that justices profit the same despite the amount of the fines.

D.

It does appear that justices might profit by issuing smaller fines.

Answer 1

Solution:-) I have used R to solve the problems, On uper side is output and on lower side is R Code.

So, scatter plot is given above

B) Now we have to test for correlation , So the hypotheses is stated as

Null hypothesis is there is a linear correlation between court incomes and justice salaries and alternative hypotheses is that there is no  linear correlation between court incomes and justice salaries and hence they did not have effect on each other.

We get the following output

t = 4.620, df = 7, p-value = 0.002

As p-value < 0.05(significance level), hence we reject the null hypothesis. Therefore,

​there is linear  correlation between court incomes and justice salaries, hence It does appear that justices might profit by levying larger fines. Option (B) is correct.