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?
1) What are the null and alternative hypotheses?
A) H0: p=0 , H1: p < 0
B) H0: p=0 , H1: p > 0
C) H0: p=0 , H1: p =/ 0
D) H0: p=/ 0 , H1: p=0
2) Construct a scatterplot.
3) The linear correlation coefficient r is
4) The test statistic t is
5) The P-value is
6) Based on the results, does it appear that justices might profit by levying larger fines?
A) It does appear that justices my profit by issuing smaller fines.
B) it does appear that justices is my profit by levying larger fines.
C) it appears that justices profit the same despite the amount of the fines.
D) it does not appear that justices might profit by levying larger fines.
X :- Court Income
Y :- Justice Salary
ΣX = 3995
ΣY = 399
ΣX * Y = 262252
ΣX2 = 4081713
ΣY2 = 21941
To Test :-
H0 :- ρ = 0
H1 :- ρ ≠ 0
r = 0.859
Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( 0.8594 * √(9 - 2) ) / (√(1 - 0.7386) )
t = 4.4473
P - value = P ( t > 4.4473 ) = 0.003
Reject null hypothesis if P value < α = 0.05 level of
P - value = 0.003 < 0.05 ,hence we reject null hypothesis
Conclusion :- There is statistical correlation between variables
B) it does appear that justices is might profit by levying larger fines.
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