Composites are materials that aremade by embedding a fiber, such as glass or car

Question

Composites are materials that aremade by embedding a fiber, such as glass or carbon, inside a matrix, such as a metal or a ceramic. Composites are used inengineering structures, and their degradation when subjected to wheather conditions is an important issue.. In an experiment to investigate the effect of the moisture on a certain kind of composite, the weight gains of a collection of n=25samples of composite subjected to water diffusion were obtained. The sample mean is x=0.358%with a sample std. of S=0.032% Can we 95% confidentfrom the results of this experiment that the average weight gain for composites of this kind is smaller than 0.37% ? {Solution Tips: Use one-sided confidence interval. Yes; if upper bound of one-sided 95% confidence interval less than 0.37 %. One sided test means that testing the statistical significance is in the one direction of interest!

Explanation / Answer

here std error =std deviation/(n)1/2 =0.0064

hence test stat t=(X-mean)/std error =(0.358-0.37)/0.0064=-1.875

for above test stat p value =0.0365

as p value is less then 0.05 level ; we reject null hypothesis and conclude that the average weight gain for composites of this kind is smaller than 0.37%

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