Answer
There is sufficient evidence to support that the mean speed is less than the speed limit.
Work Step by Step
$H_{0}:\mu=65$. $H_{a}:\mu <65.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{61.3846-65}{4.6822/\sqrt{13}}=-2.784.$ The P-value is the interval of probabilities between which the value of the test-statistic lies in the table with degree of freedom=sample size-1=13-1=12, hence P is between 0.005 and 0.01. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P is less than $\alpha=0.05$, because it is less than 0.01, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the mean speed is less than the speed limit.
