Question

the weights (in pounds) of eight vehicles and the variabilities of their braking distances (in feet) when stopping on a dry surface are shown in the table. at $alpha = 0.01$, is there enough evidence to conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry surface?

weight, x	5930	5370	6500	5100	5820	4800	5600	5910
variability, y	1.74	1.93	1.95	1.62	1.68	1.50	1.58	1.70

calculate the test statistic.
t = 2.02 (round to two decimal places as needed.)
calculate the p - value.
p - value = (round to three decimal places as needed.)

Explanation:

Step1: Determine degrees of freedom

The degrees of freedom for a correlation - t test is $n - 2$, where $n = 8$. So $df=n - 2=8 - 2 = 6$.

Step2: Use t - distribution to find P - value

We have a two - tailed test with $t = 2.02$ and $df = 6$. Using a t - distribution table or a calculator (e.g., in Python: 2*(1 - stats.t.cdf(2.02, 6)) where stats is from scipy.stats), we find the P - value.
The P - value for a two - tailed test with $t = 2.02$ and $df=6$ is $P=2\times(1 - P(T\leq|t|))$.
$P = 2\times(1 - 0.952)=2\times0.048 = 0.096$.

Answer:

$0.096$