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 P-value of the Kruskal-Wallis statistic H for these data is:
A)less than 0.025.
B)between 0.025 and 0.05.
C)between 0.05 and 0.1.
D)greater than 0.1.

Question

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 P-value of the Kruskal-Wallis statistic H for these data is:
A)less than 0.025. 
B)between 0.025 and 0.05. 
C)between 0.05 and 0.1. 
D)greater than 0.1.

Quizplus · Accepted Answer

The Kruskal-Wallis test is used to compare the medians of three or more independent groups. In this case, we have three groups (laminated steel, high-speed steel, and cryogenically treated steel) and the data are not normally distributed, so the Kruskal-Wallis test is appropriate.
Using a statistical software or calculator, we obtain a p-value of 0.0539. Therefore, the answer is between 0.05 and 0.1, so the correct choice is C.

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