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 alphaequals0.01. ​Weight, x 5930 5350 6500 5100 5870 4800 Variability in braking​ distance, y 1.71 1.95 1.93 1.65 1.68 1.50

Answer 1

From the given data, the following Table is calculated:

X	Y	XY	X2	Y2
5930	1.71	10140.3	35164900	2.9241
5350	1.95	10432.5	28622500	3.8025
6500	1.93	12545	42250000	3.7249
5100	1.65	8415	26010000	2.7225
5870	1.68	9861.6	34456900	2.8224
4800	1.50	7200	23040000	2.25
Total = 33550	10.42	58594.4	189544300	18.2464

H0: Null Hypothesis: = 0

HA: Alternative Hypothesis: 0

Test statistic is given by:

= 0.01

ndf = n - 2 = 6 - 2 = 4

From Table, critical values of t = 4.6041

Since the calculated value of t = 1.5356 is lessthan critical value of t = 4.6041, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

We cannot conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry​ surface