In the study of textiles and fabrics, the strength of a fabric is a very important consideration. Suppose that a significant number of swatches of a certain fabric are subjected to different “loads” or forces applied to the fabric. The data from such an experiment might look as follows: 

a. Make a scatterplot of the proportion failing versus the load on the fabric.

b. Using the techniques introduced in this section, calculate  for each of the loads and fit the line y = a +b(Load). What is the sig nifi cance of a positive slope for this line?

c. What proportion of the time would you estimate this fabric would fail if a load of 60 lb/sq in. were applied?

d. In order to avoid a “wardrobe malfunction,” one would like to use fabric that has less than a 5% chance of failing. Suppose that this fabric is our choice for a new shirt. To have less than a 5% chance of failing, what would you estimate to be the maximum “safe” load in lb/sq in.?

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Hypothetical Data on Fabric Strength Load (Ib/sq in.) Proportion 0.02 0.04 0.20 0.23 0.32 0.34 0.43 5 15 35 50 70 80 90 failing