Assume that the drying time for certain kind of paint under specified test conditions is known to be normally distributed with mean 75 minutes and standard deviation 5 minutes. Assume also that chemist have devised new additive that they hope will reduce the mean drying time(without changing the standard deviation). A test is then conducted to measure the drying time for a test specimen, and the company executives decide that they will be convinced that the additive is effective only if the drying time on this specimen is less than 70 minutes.
A) if the additive actually has no effect at all on the drying time, what us the probability the company executives will mistakenly conclude that it is effective? include sketch of your calculation.
B) if you want to alter the cutoff value from 70 in order to reduce the error probability in part a to .05, what
cutoff value should you choose.
C) now that suppose that the standard deviation of the drying times to 70 minutes is 2 rather than 5 minutes. without doing any new calculations, describe how this change would affect your answers to parts a and b. Give an intuitive explanation for your reasoning in both cases.