Question

The following tables shows the mpg and curbed weight, in thousands for eight randomly selected vehicles:

MPG: 28 22 20 34 41 15 19 15

Weight: 2730 2860 3140 2180 2310 4450 3920 2590

Using XLS, calculate the correlation coefficient for this sample. Using a significance of .1, test the significance of the population correlation coefficient is negatively related between mpg and curbed weight. What conclusions can you draw?

Answer 1

	MPG (X)	Weight (Y)	X * Y	X2	Y2
	28	2730	76440	784	7452900
	22	2860	62920	484	8179600
	20	3140	62800	400	9859600
	34	2180	74120	1156	4752400
	41	2310	94710	1681	5336100
	15	4450	66750	225	19802500
	19	3920	74480	361	15366400
	15	2590	38850	225	6708100
Total	194	24180	551070	5316	77457600

$r = ( ( N * \Sigma XY) - \Sigma X \Sigma Y) / (\sqrt{ (N \Sigma (X^{2}) - (\Sigma X)^{2} )(N \Sigma (Y^{2}) - (\Sigma Y)^{2} })$

Corelation Coefficient r = - 0.6825

r = ((8*551070)-194*24180)/(V(8* 5316) - (194))(8 * 77457600) – (24180)2)

To Test :-

H0 :- ρ = 0
H1 :- ρ < 0

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( -0.6825 * √(8 - 2) ) / (√(1 - 0.4658) )
t = -2.2873

Test Criteria :-
Reject null hypothesis if t < -t(α, n - 2 )
t(α, n-2) = t(0.1 , 8 - 2 ) = 1.4398
t < -t(α,n-2) = -2.2873 < -1.4398
Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 2.2873 ) = 0.0311
Reject null hypothesis if P value < α = 0.1 level of significance
P - value = 0.0311 < 0.1 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficietn evidence to conclude that negatively related between mpg and curbed weight.