Bursting strength of bottles. Polyethylene terephthalate (PET) bottles are used for carbonated beverages. A critical property of PET bottles is their bursting strength (i.e., the pressure at which bottles filled with water burst when pressurized). In the Journal of Data Science (May 2003), researchers measured the bursting strength of PET bottles made from two different designs—an old design and a new design. The data (pounds per square inch) for 10 bottles of each design are shown in the table. Suppose you want to compare the distributions of bursting strengths for the two designs. Old Design 210 212 211 211 190 213 212 211 164 209 New Design 216 217 162 137 219 216 179 153 152 217

a. Rank all 20 observed pressures from smallest to largest and assign ranks from 1 to 20.

b. Sum the ranks of the observations from the old design.

c. Sum the ranks of the observations from the new design.

d. Compute the Wilcoxon rank sum statistic.

e. Carry out a nonparametric test (at a = .05) to compare the distribution of bursting strengths for the two designs.