A production supervisor at a major chemical company wishes to determine whether a new catalyst, catalyst XA-100, increases the mean hourly yield of a chemical process beyond the current mean hourly yield, which is known to be roughly equal to, but no more than, 750 pounds per hour. To test the new catalyst, 35 trial runs using catalyst XA-100 are made. The resulting yields (in pounds per hour) are found on our Excel worksheet. Assuming all factors affecting yields of the process have been held constant as possible during the test runs, it is reasonable to regard the 35 yields obtained using the new catalyst as random samples of the population.
a. Find a 95% confidence interval for the mean of all possible yields obtained using catalyst XA-100.
b. Based on this confidence interval, can we be 95% confident that the mean yield using catalyst XA-100 exceeds 750 pounds per hour? Why?
c. As a conservative measure, let's assume that the population standard deviation is the same as the sample standard deviation. Now, determine the number of trial runs of the chemical process needed to make us 99% confident that our sample mean is within five pounds of μ.