Refer to the Composites Fabrication Magazine (Sept. 2004) evaluation of a new method of fastening fiber-reinforced polymer (FRP) strips to concrete, Exercise 2.47. Recall that a sample of 10 FRP strips mechanically fastened to highway bridges were tested for bearing strength. The strength measurement Y (in mega Pascal units, MPa) was recorded for each strip. Assume that Y is normally distributed with variance σ² = 100.

a. Describe the sampling distribution of S², the sample variance.

b. Find the approximate probability that S² is less than 16.92.

c. The data for the experiment are reproduced in the table. Do these data tend to contradict or support the assumption that σ² = 100?

Data from Exercise 2.47

Fiber-reinforced polymer (FRP) composite materials are the standard for strengthening, retrofitting, and repairing concrete structures. Typically, FRP strips are fastened to the concrete with epoxy adhesive. Engineers at the University of Wisconsin–Madison have developed a new method of fastening the FRP strips using mechanical anchors. (Composites Fabrication Magazine, Sept. 2004.) To evaluate the new fastening method, 10 specimens of pultruded FRP strips mechanically fastened to highway bridges were tested for bearing strength. The strength measurements (recorded in mega Pascal units, Mpa) are shown in the table. Use the sample data to give an interval that is likely to contain the bearing strength of a pultruded FRP strip.

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FRP 240.9 248.8 215.7 233.6 231.4 230.9 225.3 247.3 235.5 238.0