Composites are materials that are made by embedding a fiber, such as glass or carbon, inside a matrix, such as a metal or a ceramic. Composites are used in civil engineering structures, and their degradation when subjected to weather conditions is an important issue. In an experiment to investigate the effect of moisture on a certain kind of composite, the weight gains of a collection of 18 samples of composite subjected to water diffusion were obtained. The sample mean was \bar{x}= 0.337\% x - =0.337%, with a sample standard deviation of s = 0.025\%s=0.025%. (a) Is it safe to conclude from the results of this experiment that the average weight gain for composites of this kind is smaller than 0.36\%0.36%?
(b) Construct a 99\%99% confidence interval that provides an upper bound for the average weight gain for composites of this kind.