## The Annals of Mathematical Statistics

### A Sequential Decision Procedure for Choosing One of $k$ Hypotheses Concerning the Unknown Mean of a Normal Distribution

Edward Paulson

#### Abstract

A sequential procedure is given for deciding to which of $k$ non-overlapping intervals the unknown mean $\theta$ belongs which satisfies the requirement that the probability of making an incorrect decision is less than some preassigned value $\alpha$. The sequential procedure is worked out explicitly for the following two cases: (1) when $\theta$ is the mean of a normal distribution with a known variance, and (2) when $\theta$ is the mean of a normal distribution with an unknown variance. A brief discussion is also given of a related but apparently new problem, to find a sequential procedure which will simultaneously select one of the $k$ intervals and also yield a confidence interval for $\theta$ of a specified width.

#### Article information

Source
Ann. Math. Statist., Volume 34, Number 2 (1963), 549-554.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177704167

Digital Object Identifier
doi:10.1214/aoms/1177704167

Mathematical Reviews number (MathSciNet)
MR149628

Zentralblatt MATH identifier
0114.35102

JSTOR
Paulson, Edward. A Sequential Decision Procedure for Choosing One of $k$ Hypotheses Concerning the Unknown Mean of a Normal Distribution. Ann. Math. Statist. 34 (1963), no. 2, 549--554. doi:10.1214/aoms/1177704167. https://projecteuclid.org/euclid.aoms/1177704167