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. Under the null hypothesis that the three populations have the same continuous distribution:
A)H has approximately a chi-square distribution, with 3 degrees of freedom.
B)H has approximately an F(2, 6)distribution.
C)H has approximately a chi-square distribution, with 2 degrees of freedom.
D)H has a distribution that cannot be evaluated because the populations may not be Normal.

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.  Under the null hypothesis that the three populations have the same continuous distribution:
A)H has approximately a chi-square distribution, with 3 degrees of freedom. 
B)H has approximately an F(2, 6)distribution. 
C)H has approximately a chi-square distribution, with 2 degrees of freedom. 
D)H has a distribution that cannot be evaluated because the populations may not be Normal.

Quizplus · Accepted Answer

The null hypothesis comparing continuous distributions of three or more groups is tested using the Kruskal-Wallis test. This test is a non-parametric alternative to the one-way ANOVA test, which assumes normality and equal variances. The Kruskal-Wallis test uses the rank sums of the observations to test for differences between the groups. Under the null hypothesis, the test statistic H has approximately a chi-square distribution with k-1 degrees of freedom, where k is the number of groups. In this case, k=3, so the degrees of freedom of H are 2. Therefore, the correct choice is C.

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