Question

The weights​ (in pounds) of

six

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

alphaαequals=0.01

Weight, x   Variability in braking distance, y
5990   1.74
5320   1.99
6500   1.88
5100   1.63
5810   1.62
4800   1.5

set up the hypothesis for the test.

identify the critical values

Select the correct choice below and fill in any answer boxes within your choice.

​(Round to three decimal places as​ needed.)

(A. the critical values are -to=___ and to=___

B. the critical value is____

calculate the test statistic

t=____

what is your conclusion?

There (is/isnot) enough evidence at the 1% level of significance to conclude that there (is/is not) a significant linear correlation between vehicle weight and variability in braking disnace on *a dry surface*

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Answer 1

	Weight X	Breaking Distance Y	X * Y
	5990	1.74	10422.6	35880100	3.0276
	5320	1.99	10586.8	28302400	3.9601
	6500	1.88	12220	42250000	3.5344
	5100	1.63	8313	26010000	2.6569
	5810	1.62	9412.2	33756100	2.6244
	4800	1.5	7200	23040000	2.25
Total	33520	10.36	58154.6	1.89E+08	18.0534

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 1.1086

Test Criteria :-
Reject null hypothesis if

The critical values are -to= -4.6041 and to= 4.6041

-4.6041 < 1.1086 < 4.6041
Result :- We fail to Reject null hypothesis

Decision based on P value
P - value = P ( t > 1.1086 ) = 0.3298
Reject null hypothesis if P value <    level of significance
P - value = 0.3298 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- We Accept H0

There is statistically no linear correlation between variables.

There ( is not ) enough evidence at the 1% level of significance to conclude that there ( is ) a significant linear correlation between vehicle weight and variability in braking distance on *a dry surface*.