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 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 1130.0 274.0 254.0 111.0 151.0 30.0 Justice Salary 30 42 92 58 44 60 24 25 18

What are the null and alternative​ hypotheses? A. Upper H 0 ​: rho equals 0 Upper H 1 ​: rho less than 0 B. Upper H 0 ​: rho not equals 0 Upper H 1 ​: rho equals 0 C. Upper H 0 ​: rho equals 0 Upper H 1 ​: rho not equals 0 D. Upper H 0 ​: rho equals 0 Upper H 1 ​: rho greater than0

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

0.05

​,

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

alpha

equals0.05

.

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

Ans:

linear correlation coefficient r is=0.882

n=9

test statistic t is:

t=0.882*sqrt((9-2)/(1-0.882^2))

t=4.953

df=9-2=7

p-value=tdist(4.953,7,2)=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 for a significance level of alpha=0.05

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