Waste is an important factor to monitor in many manufacturing processes. When the variability of material used in a process is too high, engineers often must make changes to the process to avoid expensive wastage. An anti-rust spray uses a liquid that is sprayed on all surfaces of a certain type of racing car, and the amount used on each car was determined to be a normally distributed random variable. You recorded the fluid amount sprayed on each car of a randomly selected sample of 25 cars to have a sample mean =100 fluid ounces and a sample standard deviation of S= 20.4025 fluid ounces. a) Test the hypothesis that the true mean of sprayed amount H0: = 100 versus: H1: < 100 using = 0.05. (5 marks)

b.b) What is the P-value of the test in part a) above?c) Compute the power of the test if the true mean amount is as high as 98.4 fluid ounce. [You can determine it by any method or tool you want]d) Show how the question in part (a) could be answered by constructing one-sided confidence bound on the mean speed.e) Is there strong evidence to conclude that the variance in this experiment is less than 529? Use = 0.05. (5 marks)