Question: A clerk in the admissions office at Small State University processes requests for admissions materials. The time to process requests depends on the program of interest (e.g., industrial engineering, management science, computer science, etc.) and on the level of the program (Bachelors, Masters, Ph.D.). Suppose that the processing time is modeled well as normally distributed, with mean 7 minutes and standard deviation 2 minutes. At the beginning of the day it takes the clerk some time to get set to begin working on requests; suppose that this time is modeled well as exponentially distributed, with mean 20 minutes. The admissions office typically receives between 40 and 60 requests per day. Let X be the number of application S received On a day, and let f be the time required tO process them (including the set-up time). Fit a meta model for E(Y!x) by making n replications at the design points x = 40, 50, 60. Notice that, in this case, we know that the correct model is
E(Y|x) = ß0 + ß1x = 20 + 7x
(Why? ) Begin with n = 2 replications at each design point and estimate ß1 and ß2 Gradually increase the number of replications and observe how many are required for the estimates to be close to the true values.