Consider a sample of size 36 with $mean=10$ and $variance=144$, that is collected from some (larger) population.

It is easily verified that, when $t$ is a random variable with a probability density function that follows a $t$-distribution with 35 degrees of freedom, $P(t > 2.5)=.00863$.

Determine the $p_{value}$ associated with conducting a Hypothesis Test with a $99\%$ level of confidence to test $H_0: \mu=5$ versus $H_a: \mu>5$.