A Tool Manufacturer Tests Three Types of Cutters Used in a Lathe

Multiple Choice

A tool manufacturer tests three types of cutters used in a lathe operation. One type is a laminated steel cutter made of very hard high-carbon steel sandwiched between two softer steels. Another is a special high-speed steel cutter developed using powder metallurgy. The final one is made from cryogenically treated steel. Cutters of each type are tested to see how long they will last (in hours) in continuous operation until they need to be sharpened. The times are recorded for each cutter used in the study, and the results are given below. The data are to be analyzed with the Kruskal-Wallis test. The null hypothesis is that the time until sharpening is needed has the same distribution in all groups. The alternative is:

A) mean time until sharpening is needed is systematically higher in some groups than others.
B) not all three mean times until sharpening is needed are equal.
C) the mean times until sharpening are different in each of the three groups of cutter type.
D) the times until sharpening is needed are systematically longer for cryogenically treated steel cutters than for the other two types of cutters.