A mechanical engineer wishes to compare strength properties of steel beams with similar beams made with a particular
alloy. The same number of beams, n, of each type will be
tested. Each beam will be set in a horizontal position with a
support on each end, a force of 2500 lb will be applied at the
center, and the deflection will be measured. From past experience
with such beams, the engineer is willing to assume
that the true standard deviation of deflection for both types
of beam is .05 in. Because the alloy is more expensive, the
engineer wishes to test at level .01 whether it has smaller
average deflection than the steel beam.