In a chemical process the amount of a certain type of impurity in the output is difficult to control is thus a random variable. Speculation is that the population mean amount of the impurity is 0.20 grams per gram of output. It is known that the standard deviation is 0.1 grams per gram of output. An experiment is conducted to gain more insight regarding the speculation that the population mean is 0.20.
a) The process was run on a lab scale 50 times and the sample average x(bar) turned out to be 0.23 grams per gram. Perform analysis and comment on the speculation on the population mean.
b) What if the process was run 30 times and the sample average x(bar) turns out to be 0.19 grams per gram?