14. The article Evaluating Tunnel Kiln Performance

(Amer. Ceramic Soc. Bull., Aug. 1997: 59—63) gave the following summary information for fracture strengths (MPa) of n  169 ceramic bars red in a particular kiln: , s  3.73.

a. Calculate a (two-sided) con dence interval for true average fracture strength using a con dence level of 95%. Does it appear that true average fracture strength has been precisely estimated?

b. Suppose the investigators had believed a priori that the population standard deviation was about 4 MPa. Based on this supposition, how large a sample would have been required to estimate m to within .5 MPa with 95% con dence?