A manufacturer needs to buy aluminum sheets with an average thickness of 0.05 inches. The manufacturer knows that significantly thinner sheets would be unsafe and considerably thicker sheets would be too heavy. A random sample of 100 sheets from a potential supplier is collected. The thickness of each sheet in this sample is measured (in inches) and the mean of the sample is 0.0474. Should the manufacturer buy aluminum sheets from this supplier? Assume a significance level of 0.05 and please show the work.