The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. They will choose to use the preservative that can keep the meat fresh for the longest amount of time. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. Suppose the variability of the number of hours until spoilage is the same for meat treated by both preservatives but the normal probability plots reveal that the number of hours until spoilage is right-skewed for the 15 cuts treated by preservative I and left-skewed for the 15 cuts treated with preservative II. Which of the following tests will be the most appropriate?
A) pooled-variance t test
B) Wilcoxon signed rank test
C) Wilcoxon rank sum test
D) paired t test

Question

Quizplus · Accepted Answer

The Wilcoxon rank sum test is appropriate for comparing the central tendencies of two independent samples when the assumptions of a t-test are not met (such as when the distributions are skewed). The fact that the normal probability plots reveal different skews for the two preservatives suggests that a parametric test (like a paired t-test or pooled-variance t-test) may not be appropriate. The Wilcoxon signed rank test is only appropriate for comparing the central tendencies of paired samples, which is not the case here. Therefore, the Wilcoxon rank sum test is the most appropriate choice.

The Use of Preservatives by Food Processors Has Become a Controversial