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 - test is $n - 2$, where $n$ is the number of data - pairs. Here, $n = 8$, so $df=n - 2=8 - 2 = 6$.

Step2: Calculate the P - value

We know the test - statistic $t = 2.02$ and $df = 6$. Since this is a two - tailed test for correlation, we use the t - distribution to find the P - value. Using a t - distribution table or a calculator with a t - distribution function (e.g., in Excel: =2*(1 - T.DIST(ABS(2.02),6,TRUE))), we find the P - value.
The P - value for a two - tailed test with $t = 2.02$ and $df=6$ is $P - value=0.096$.

Answer:

$0.096$