This is a Quality Control Problem. Please fully answer the question with all work for thumbs up! Thanks

(Data is Given)

Two observable quality characteristic 21 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: 55 200 130 and S 30 130 120 (a) Determine the UCL for a Hotelling T2 control chart. Consider a = = 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 T2 for these 15 samples. Based on the UCL from part (a), do you see any out of control samples? 11 Table 1: Data for Exercise 4(b) Sample Number | 21 | 22 | Sample Number 1 2 1 | 58 | 32 | 9 | 46 | 25 2 | 60 | 33 | 10 | 50 | 29 3 | 50 | 27 | | 49 | 27 4 | 54 | 31 | | 57 | 30 5 | 63 | 38 | 13 58 | 33 6 | 53 | 30 14 75 45 7 | 42 | 20 | 15 | 55 | 27 8 | 55 | 31 | | 12