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 significane of alphaαequals=0.01

Weight, x	Variability in braking distance, y
5910	1.74
5330	1.93
6500	1.93
5100	1.64
5870	1.67
4800	1.5

How would you get critical values AND the t-values/test statistic ?

Answer 1

To find out the correlation coefficient, I have used Minitab Software -> stat - > Basic statistics -> correlation

Let denotes the true correlation between vehicle weight and variability in braking distance on a dry​ surface.

To test against

Here

sample correlation coefficient r = 0.646

and sample size n = 6

The test statistic can be written as

which under H₀ follows a t distribution with df.

We reject H₀ at 1% level of significance if

Now,

The value of the test statistic

and critical value

Since , so we fail to reject H₀ at 1% level of significance and we can conclude that there is no significant  linear correlation between vehicle weight and variability in braking distance on a dry​ surface.

For critical value : Calc -> Probability distributions -> t -> Inverse cumulative distribution