1. Some researchers have conjectured that stem-pitting disease in peach tree seedlings might be controlled with weed and soil treatment. An experiment was conducted to compare peach tree seedling growth with soil and weeds treated with one of two herbicides.
In a field containing 10 seedlings, six were randomly selected throughout the field and assigned to receive Herbicide A. The remaining seedlings were to receive Herbicide B. Soil and weeds for each seedling were treated with the appropriate herbicide, and at the end of the study period the height (in cm) was recorded for each seedling. The following results were obtained:
If W, the Wilcoxon rank sum test statistic, is the sum of the ranks assigned to group Herbicide A, then W has mean μW and standard deviation σW
A. μW = 33 and σW = 4.69
B. μW = 33 and σW = 22
C. μW = 22 and σW = 4.69
2. Suppose we are comparing two formulations of a sun block for moisturizing ingredients. For each of 20 subjects a coin is flipped. If the coin comes up heads, the subject uses Formulation A on the left side of their back and Formulation B on the right side. If the coin comes up tails, the subject uses Formulation B on the left side of their back and Formulation A on the right side. Skin dryness scores are obtained for each formulation. We wish to test the hypotheses:
H0: The scores have the same distribution for both formulations.
Ha: The scores are systematically higher for either Formulation A or Formulation B.
The Wilcoxon signed rank test is computed for the data and gives a value W + = 161.5. Using the Normal approximation (without the continuity correction) the P-value is
A. 0.0087.
B. 0.0174.
C. 0.0348.