4. (20 points) A civil engineer wants to compare two machines for grinding cement and sand. A sample of a fixed quantity of cement and sand is taken and put in each machine. The machines are run and the fineness of each mixture is noted. This process is repeated five times. The results, in microns, are as follows: Machine 1 (X) 7 9 6 8 4 Machine 2 (Y) 3 5 3 6 9 Assume that the differences in machine readings have a normal distribution. (a) (10 points) Find a 99% confidence interval for the mean difference, /1 - /2, in machine readings. (b) (10 points) Test with o = 0.01, that the mean difference is zero versus a two-sided alternative