In the study of textiles and fabrics, the strength of a fabric is a very important consideration. Suppose that a sig nifi cant 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:

Hypothetical Data on Fabric Strength Load

(lb/sq in.)

5 15 35 50 70 80 90 Proportion failing 0.32 0.34 0.43

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

b. Using the techniques introduced in this section, calcu-

late yr 5 lna p 1 2 p b for each of the loads and fit the line yr 5 a 1 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.?