## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 20, Number 4 (1949), 540-551.

### The Power of the Classical Tests Associated with the Normal Distribution

#### Abstract

The present paper is concerned with the power function of the classical tests associated with the normal distribution. Proofs of Hsu, Simaika, and Wald are simplified in a general manner applicable to other tests involving the normal distribution. The set theoretic structure of several tests is characterized. A simple proof of the stringency of the classical test of a linear hypothesis is given.

#### Article information

**Source**

Ann. Math. Statist., Volume 20, Number 4 (1949), 540-551.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177729946

**Digital Object Identifier**

doi:10.1214/aoms/1177729946

**Mathematical Reviews number (MathSciNet)**

MR32171

**Zentralblatt MATH identifier**

0035.08902

**JSTOR**

links.jstor.org

#### Citation

Wolfowitz, J. The Power of the Classical Tests Associated with the Normal Distribution. Ann. Math. Statist. 20 (1949), no. 4, 540--551. doi:10.1214/aoms/1177729946. https://projecteuclid.org/euclid.aoms/1177729946