The$$quality$-$control manager at a compact fluorescent light

bulb$($CFL$)$ factory needs to determine whether the mean life

of a large shipment of CFLs is equal to$7,525$ hours. The population standard deviation is

$100$hours$.$ A random sample of $64$ light bulbs indicates a

sample mean life of $7,500$ hours.a$.$ At the $0\mathrm{.}05$ level of$$significance$,$ is

there evidence that the mean life is different from

$7,525$hours$?$b$.$ Compute the$$p$-$value and interpret its

meaning.c$.$ Construct a $95\%$ confidence interval

estimate of the population mean life of the light bulbs.d$.$ Compare the results of$($a$)$

and$($c$).$ What conclusions do you$$reach$?$