6. Dead pixels are a big problem in manufacturing computer and cell phone screens. The physics of the manufacturing process dictates that dead pixels happen according to a spatial Poisson process, so that the numbers of dead pixels in cell phone screens are independent Poisson random variables with parameter A, the expected number of dead pixels. Naturally, A depends on details of how the screens are manufactured. In an effort to reduce the expected number of dead pixels, six assembly lines were set up, each with a different version of the manufacturing process. A random sample of 50 phones was taken from each assembly line and sent to the lab for testing. Mysteriously, three phones from one assembly line disappeared in transit, and 15 phones from another assembly line disappeared. Sample sizes and sample mean numbers of dead pixels appear in the table below. Manufacturing Process 1 2 3 4 5 6 ybar 10.68 n 50 9.87234 9.56 8.52 10.48571 9.98 47 50 50 35 50 (a) What is the parameter space ?? (b) We want to know whether the expected number of dead pixels is different for the six manufacturing processes. What is the null hypothesis, in symbols? Use Greek letters. (c) What is the alternative hypothesis? (d) What is o? (e) What is ₁? (f) What is ? The answer is numerical. Note that it is a point in the parameter space. (g) What is o? The answer is numerical. Like 6, it is a point in the parameter space. (h) Give a formula for G². Keep simplifying! (i) Calculate G2 for the data above. (j) What are the degrees of freedom? (k) What is the critical value at a = 0.05? (1) Do you reject Ho? Answer Yes or No. (m) Is a directional conclusion possible here? Answer Yes or No. (In practice we would follow up with tests comparing all (2) pairs of means.)