This test is to be written in the BSB Student Technology Centre. The duration of the test is 2 hours.
Any aids and resources are permitted. You may consult any web pages but you may not use e-mail or communicate with anyone other than the instructor.
Part A.
Let X be a single observation from a Poisson distribution with mean lambda. Derive two-sided confidence intervals for lambda using
For each formula, draw a graph plotting actual coverage against the true value of lambda.
Part B.
The numbered problems are from Agresti, A. (1996), An Introduction to Categorical Data Analysis, Wiley.
Chapter 1
1.8, 1.9
Chapter 2
2.9 [Include, if possible, a P-value or confidence interval for part b.]
2.19a, 2.19b [Suggestion: you can save calculation time by using the R functionchisq.test()
.]