Meeting specifications: Two extrusion machines that manufacture steel rods are being compared. In a sample of 1000 rods taken from machine A, 960 met specifications regarding length and diameter. In a sample of 600 rods taken from machine B, 582 met the specifications. Machine B is more expensive to run, so it is decided that machine A will be used unless it can be convincingly shown that machine B produces a larger proportion of rods meeting specifications.

a. State the appropriate null and alternate hypotheses for making the decision as to which machine to use.

b. Perform a hypothesis test at the α = 0.05 level to determine which machine to use. State your conclusion.