# The weights​ (in pounds) of 6

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 ?

To find out the correlation coefficient, I have used MinitabSoftware -> stat – > Basic statistics -> correlation

Let denotes the true correlation between vehicle weight andvariability 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 significanceand we can conclude that there is no significant  linearcorrelation between vehicle weight and variability in brakingdistance on a dry​ surface.

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

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