FIXED LENGTH SEQUENTIAL CONFIDENCE INTERVALS FOR THE PROBABILITY OF RESPONSE

Abstract

In this paper we present a fixed length confidence interval for a proportion, using the distribution of the terminal point under a stopping rule. We will show that under a natural order restriction on the set of terminal points given by the stopping rule we are able to use the distribution of the terminal point to calculate a confidence interval in a way similar to what we use in the fixed sample size case. We then select a stopping rule which gives at most the correct length of the confidence interval.

Keywords:

• Exact
• Proportion
• Bernoulli distribution
• Stochastic monotonicity
• Stopping rule

ACKNOWLEDGMENT

This material is a part of my thesis, and I am very grateful to my supervisor prof. Sture Holm for suggesting the topic. I am also very grateful for the comments and suggestions received from the referee.