Questions 2. An experimenter wishes to compare the number of bacteria of types A and B in a water source. A total of n independent water samples are taken from the source, and counts are made for each sample. Let X; denote the number of type A bacteria and Y; denote the number of type B bacteria for sample i. Assume that the two bacteria types are sparsely distributed within a water sample so that X1, X2,, X and Y₁, Y2,..., Yn can be considered independent random samples from Poisson distributions with means ₁ and λ2, respectively. n 1. Find the MLE of 7 = 1/(\1 + 2) and show that it is consistent. Solution: 2. Using asymptotic properties of the maximum likelihood estimators and the 8-method find an approximate pivotal quantity and make a 100 ×(1-a)% confidence interval for T. Solution:

Question No. 4:   According to the All Pakistan Software Developer Association (APSDA), developers generally spend more than 40 hours each week working on software and web development. The Table 4.1 shows the number of hours worked per week for a sample of 15 Software developers and a sample of 10 Web developers.   Table 4.1 Software Developers 56 54 54 49 61 48 58 60 59 53 50 58 55 57 52 Web Developers 47 50 46 47 48 49 46 55 44 42 ----     a)      What is the third quartile of spending working hours for Software developers?   b)      Create a box plot for the number of hours worked for Software developers.   c)      Create a box plot for the number of hours worked for Web developers.   d)      Comment on the differences between the box plots for Software & Web developers.

Question 4a. A large accountancy firm finds that over the long run 10% of its statements for clients are in error in some way. A quality assurance officer at the firm investigating the source of the errors takes a sample of 20 statements produced by a single employee and classifies each as being “in error” or “not in error”.i. If the variable X is used to represent the number of statements in the sample that are in error, and assuming the error rate is the firm’s level of 10% then state:• the type of distribution this variable has; and• the parameter/s of this distribution. ii. Determine the probability that 2 or less returns in this sample are in error. The quality assurance officer found that there were 5 statements in the sample that were in error.iii. Determine the probability of finding 5 or more returns in error if indeed the error rate was 10%. iv. Based upon your answer for part iii., what conclusion might the quality assurance office make about this employee in terms of the…

Suppose that a region has two hospitals.  Hospital A has about 10 births per day, and hospital B has about 50 births per day.  About 50% of all babies are boys, but the percentage who are boys varies at each hospital from day to day.  Over the course of a year, which hospital will have more days on which 60% or more of the births are boys? The smaller Hospital A, the larger B, or will Hospital A and B have nearly the same number of days?