A scientist wants to compare the densities of two cylinders, but one is twice as high and has a diameter two times as long as the other. How should the scientist compare the two densities of the cylinders if he doesn't know the volume of the larger cylinder? If the volume of the smaller cylinder is 30 cm^3, what is the volume of the larger cylinder?

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.