Question 16.51

16.51 Decay of polyester fabric.

In Exercise 16.17 (page 16-13), the breaking strengths (in pounds) of strips of polyester fabric buried in the ground were considered for two time points. Breaking strength is a good measure of the extent to which the fabric has decayed. Here are the breaking strengths for several lengths of time.18

poly2

Time Breaking strength
2 weeks 118 126 126 120 129
4 weeks 130 120 114 126 128
8 weeks 122 136 128 146 131
16 weeks 124 98 110 140 110
  1. Find the standard deviations of the four samples. They do not meet our rule of thumb for applying ANOVA. In addition, the sample buried for 16 weeks contains an outlier. We will use the Kruskal-Wallis test.

    16-29

  2. Find the medians of the four samples. What are the hypotheses for the Kruskal-Wallis test, expressed in terms of medians?
  3. Carry out the test and report your conclusion.

16.51

(a) The standard deviations are 4.60, 6.54, 9.04, 16.09. (b) The medians are 126, 126, 131, 110. H0: The median breaking strength for all groups are the same. Ha: Some medians are higher in some groups than in others. (c) , . The data do not show median breaking strength differences across different times; there appears to be no decay.