Statistics 4F03/6F03 - Test #1

2005-10-13 17:00-19:00

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

  1. The normal-approximation pivotal quantity (X - lambda)/sqrt(X) with continuity correction;
  2. The normal-approximation pivotal quantity (X - lambda)/sqrt(lambda) without continuity correction;
  3. A "mid-P" definition based on exact Poisson tail probabilities.

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 function chisq.test().]

Statistics 4F03/6F03