Based on a correlation test, there is enough evidence to support a significant linear correlation between vehicle weight and variability in braking distance on a wet surface at a=0.01.
A correlation test can be performed to determine if there is a significant linear correlation between vehicle weight and variability in braking distance.
A calculator or statistical software shows that the correlation coefficient (r) between the weight and variability is 0.872.
The critical value approach helps us to test if this correlation is significant at a = 0.01 with n = 8 (number of data points), the critical value of r at a = 0.01 is 0.784.
The calculated correlation coefficient = 0.872
Thus, since the correlation coefficient is greater than the critical value (0.784), we can conclude that there is enough evidence to support a significant linear correlation between vehicle weight and variability in braking distance on a wet surface at a=0.01.
Complete Quesiton:
The weights (in pounds) of eight vehicles and the variabilities of their braking distances (in feet) when stopping on a wet surface are shown in the table.
Weight (x) Variability (v)
5900 2.92
2400 2.45
6500 4.04
5100 1.77
5800 2.86
4800 2.31
5700 2.79
5820 2.78
At a=0.01 is there enough evidence to conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a wet surface?