## The Annals of Statistics

### One-Sample $t$-Test When Sampling from a Mixture of Normal Distributions

#### Abstract

For the one-sample $t$-test a new form of the exact distribution of the test statistic $t^2$ is obtained when sampling from a distribution which is a mixture of two normal distributions. A numerical example is provided to show that the size of the test can differ greatly when sampling from distributions having the same skewness and kurtosis. Contours of equal size are plotted for a particular case in a certain cross section of the parameter space.

#### Article information

Source
Ann. Statist., Volume 5, Number 4 (1977), 803-807.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343904

Digital Object Identifier
doi:10.1214/aos/1176343904

Mathematical Reviews number (MathSciNet)
MR501510

Zentralblatt MATH identifier
0378.62015

JSTOR
Lee, Austin F. S.; Gurland, John. One-Sample $t$-Test When Sampling from a Mixture of Normal Distributions. Ann. Statist. 5 (1977), no. 4, 803--807. doi:10.1214/aos/1176343904. https://projecteuclid.org/euclid.aos/1176343904