Answer
a) $P-value =0.009$.
b) The null hypothesis should be rejected and this means that the breaking strength is not 800 pounds.
Work Step by Step
Given that, $\mu=800, \sigma=12, n=20, \bar x =793$, then,
$H_{0}:\mu=800.\\ H_{1}:\mu \ne 800.$
$Z=\frac{\bar x- \mu}{\frac{\sigma}{\sqrt{n}}}=\frac{793- 800}{\frac{12}{\sqrt{20}}}\approx -2.61$
$P-value =2\times(1-P(Z\leq 2.61)=2\times(1-0.9955)=0.009$
Since $\alpha=0.01$ and $P-value =0.009$ , the null hypothesis is rejected
