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
65.0   31
403.0   46
1567.0   93
1130.0   54
270.0   44
253.0   62
112.0   25
155.0   26
30.0   17

What are the null and alternative​ hypotheses?

A.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρnot equals≠0

B.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρless than<0

C.

Upper H 0H0​:

rhoρnot equals≠0

Upper H 1H1​:

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

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: (260, 84); (420, 24); (640, 56); (760, 86); (880, 48); (900, 34); (1040, 86); (1260, 46); (1480, 18).

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: (40, 18); (60, 32); (120, 26); (160, 26); (260, 62); (280, 44); (400, 46); (1140, 54); (1560, 94).

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

▼

greater

less

than the significance level

0.050.05​,

there

▼

is

is not

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 not appear that justices might profit by levying larger fines.

C.

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

D.

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

Answer 1

Let independent variable (X): Court_Income

Dependent variable (Y): Justice_Salary

Following is the scatter plot:

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	65	31	4225	961	2015
	403	46	162409	2116	18538
	1567	93	2455489	8649	145731
	1130	54	1276900	2916	61020
	270	44	72900	1936	11880
	253	62	64009	3844	15686
	112	25	12544	625	2800
	155	26	24025	676	4030
	30	17	900	289	510
Total	3985	398	4073401	22012	262210

------------------------------------------------

Correct option:

A.

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