Assume That a Simple Random Sample Has Been Selected from a Normally

Essay

Assume that a simple random sample has been selected from a normally distributed population and test the given claim.
Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim.
-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.