A new centrifugal pump is being considered for an application involving the pumping of ammonia. The specification is that the flow rate be more than \(5 \mathrm{gal}-\) lons per minute (gpm). In an initial study, eight runs were made. The average flow rate was \(6.5 \mathrm{gpm}\) and the standard deviation was \(1.9 \mathrm{gpm}\). If the mean flow rate is found to meet the specification, the pump will be put into service.

a. State the appropriate null and alternative hypotheses.

b. Find the \(P\)-value.

c. Should the pump be put into service? Explain.