Question

The weights (in pounds) of 6 vehicles and the variability of their braking distances (in feet) when stopping on a dry surface are shown in the table. Can you conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry surface? Use alpha = 0.01

Weight, x 5940 5390 6500 5100 5820 4800

Variability in braking distance, 1.74 1.92 1.93 1.61 1.69 1.50

y

Setup the hypothesis for the test

H0: p ___ 0

Ha: P___ 0

Identify the critical value(s). Round to three decimal places as needed.

Calculate the test statistic.

Answer 1

	Weight X	Breaking Distance Y	X * Y
	5940	1.74	10335.6	35283600	3.0276
	5390	1.92	10348.8	29052100	3.6864
	6500	1.93	12545	42250000	3.7249
	5100	1.61	8211	26010000	2.5921
	5820	1.69	9835.8	33872400	2.8561
	4800	1.5	7200	23040000	2.25
Total	33550	10.39	58476.2	1.9E+08	18.1371

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 2.075

Test Criteria :-
Reject null hypothesis if

Critical value

-4.6041 < 2.075 < 4.6041
Result :- We fail to Reject null hypothesis

Decision based on P value
P - value = P ( t > 2.075 ) = 0.1066
Reject null hypothesis if P value < level of significance
P - value = 0.1066 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- We Accept H0

There is no linear correlation between variables.