Question: In a certain department a pilot study is carried out to assess the quality perfor mance. The department is composed of 25 parallel machines operating in 2 shifts. A new quality scoring system is developed which rates each batch of product on a scale of 10. Data for 8 batches were collected. Two machines are randomly selected. For each machine, two random batches are selected for day time and evening shifts. The quality scores obtained are given in the Table. They expect to have a current score of 6 and desire to improve this value to 7 in two months time. Their target is 9 in one year period. Shift Mi MI Evening 3,5 6,5 Day 6,6 9,8 a) What is the design of experiments? b) Considering the three models as I. Y = 4+E II. Y = + + + III. Y = # ++9+ where the parameters designate the overall mean, machine and shift effects. The error term is assumed to be i.i.d. Normal random variable with constant variance. That is En IID Normal(0,0%), carry out the analysis in following stages 1. Estimate the parameters and obtain the algebraic breakdown of each observation 2. Obtain degrees of freedom for each vector 3. Obtain magnitude of each vector? What does it corresponds to? 4. Perform a statistical test to draw conclusions on the proposed models. a