The following are the number of mistakes (x) made in five successive weeks by fo

Question

The following are the number of mistakes (x) made in five successive weeks by four technicians working for a medical laboratory: (A) The statistical model for the data above is x_ij = mu +alpha, + e_ij (i = l, .. k: j = l, .., n) where mu, alpha_i 's are unknown parameters (subject to sigma^k_i = 1 alpha_i = 0) and e_ij are uncorrelated random errors with E(e_ij) = 0 and var (e_ij) = sigma^2. The least squares estimates of the parameters are mu = mean of all observations, alpha_i = mean of observations for i-th treatment - mean of all observations. Compute mu and alpha (i = 1, 2, 3, 4).

Explanation / Answer

Mean of all observations = sum of all observations/ NUmber of total observations ^ = (70 + 75 + 79 + 69)/20= 14.65

treatment 1 = (70/5) - 14.65 = -0.65

treatment 2 = (75/5) - 14.65 = 0.35

treatment 1 = (79/5) - 14.65 = 1.15

treatment 1 = (69/5) - 14.65 = -0.85

Tech 1 Tech 2 Tech 3 Tech 4 13 14 13 18 16 16 18 10 12 11 16 14 14 19 14 15 15 15 18 12 Total 70 75 79 69

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