3. (25 pts) Two observable quality characteristic z, and 22 of a production process is recorded for m = 50 samples with a sample size of n = 25. Assume that mean values of the quality characteristics and the covariance matrix were determined as: 200 130 I = 130 120 (a) Determine the UCL for a Hotelling Tz control chart. Consider o = 0.001. (b) The first 15 samples of the data is shown in Table 1. The data are sample means of each quality characteristic. Determine the 72 for these 15 samples. Based on the UCL from part (a), do you see any out of control samples? Table 1: Data for Exercise 4(b) Sample Number | 21 | $2 Sample Number 21 $2 58 32 9 46 25 2 60 33 10 50 29 3 50 27 11 49 27 4 54 31 12 57 30 5 63 38 13 58 33 6 53 30 14 75 45 -J 42 20 15 55 27 8 55 31