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 alphaequals0.05. 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 1567.0 1131.0 273.0 251.0 112.0 150.0 32.0 Justice Salary 31 45 92 58 48 60 26 27 19

What are the null and alternative​ hypotheses?

A.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρless than<0

B.

Upper H 0H0​:

rhoρnot equals≠0

Upper H 1H1​:

rhoρequals=0

C.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρnot equals≠0

D.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρgreater 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: (220, 84); (220, 80); (360, 80); (400, 70); (580, 84); (740, 58); (1080, 62); (1120, 30); (1420, 44).

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: (40, 20); (60, 32); (120, 26); (160, 28); (260, 60); (280, 48); (400, 46); (1140, 58); (1560, 92).

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: (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 appears that justices profit the same despite the amount of the fines.

B.

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

C.

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

D.

It does not appear that justices might profit by levying larger fines.

Click to select your answer(s).

Answer 1

null hypothesis: Ho:               ρ	=	0
Alternate Hypothesis: Ha: ρ	≠	0

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.875

test stat t=

r*(√(n-2)/(1-r2))=

4.789

P value    =

0.002

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

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