An electronics manufacturing process has historically had a mean completion time of $70$ minutes. It is claimed that, due to improvements in the process, the mean completion time, $,$ is now less than $70$ minutes. A random sample of $10$ completion times using the new process is taken. The sample has a mean completion time of $69$ minutes, with a standard deviation of $10$ minutes.

Assume that completion times using the new process are approximately normally distributed. At the $0\mathrm{.}10$ level of significance, can it be concluded that the population mean completion time using the new process is less than $70$ minutes?

Perform a one$-$tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places. $($If necessary, consult a list of formulas.$)$

$($a$)$ State the null hypothesis $H_0$ and the alternative hypothesis $H_1$

$H_0$

$H_1$

$($b$)$ Determine the type of test statistic to use.

$($c$)$ Find the value of the test statistic. $($Round to three or more decimal places.$)$

$($d$)$ Find the $p-$value. $($Round to three or more decimal places.$)$

$($e$)$ Can it be concluded that the mean completion time using the new process is less than $70$ minutes?