Exam 15: Nonparametric Tests

The use of carpeting in hospitals, while having aesthetic value, raises an obvious question: Are carpeted floors sanitary? An experiment comparing airborne bacteria levels in carpeted rooms with that in uncarpeted rooms was performed in an effort to answer this question. Specifically, for each of eight carpeted rooms and eight uncarpeted rooms in a hospital, the number of bacteria per cubic foot of air was measured. The data are given below. Assume that room sizes are equal, and that the 16 rooms in this experiment were assigned randomly to the carpet and no-carpet groups. When ranking all the observations together, the bacteria count ranked 12th is:

Which of the following is part of the signed rank test?

The Wilcoxon rank sum test for comparing two independent samples tests which of the following hypotheses?

In a study to investigate the effect of regular exercise on raising HDL (good cholesterol) levels, a random sample of five male subjects known to have low HDL levels had their HDL measured. After six months on a regular exercise schedule, it was measured again. The data are given in the following table. How do you know that the data should be analyzed using the Wilcoxon signed rank test?

Which of the following is false?

In a study to investigate the effect of regular exercise on raising HDL (good cholesterol) levels, a random sample of five male subjects known to have low HDL levels had their HDL measured. after six months on a regular exercise schedule, it was measured again. The data are given in the following table. The standardized value z of the Wilcoxon signed rank test W⁺ is:

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:

The alternative hypothesis for the Kruskal-Wallis test is typically: