Solve the Problem $$\begin{array} { l l l l l } 518 & 548 & 561 & 523 & 536 \\499 & 538 & 557 & 528 & 563\end{array}$$

Essay

Solve the problem.
-In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is
made which is supposed to increase the time between failures. Tests on a random sample of 10 modified
components resulted in the following times (in hours) between failures. $$\begin{array} { l l l l l } 518 & 548 & 561 & 523 & 536 \\499 & 538 & 557 & 528 & 563\end{array}$$ At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is
greater than 520 hours. Use the P-value method of testing hypotheses.