Antwan determines the distance between the points –7 and 2 on a numberline. Maggie determines the difference between the numbers –7 and 2. How are Antwan's and Maggie's solutions related? Maggie's solution is the absolute value of Antwan's solution. Antwan's solution is the absolute value of Maggie's solution. Both solutions are greater than either of the two numbers in the problem. Both solutions are less than either of the two numbers in the problem.

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.