## Abstract

An overview of hypothesis testing for the common mean of independent normal distributions is given. The case of two populations is studied in detail. A number of different types of tests are studied. Among them are a test based on the maximum of the two available t-tests, Fisher's combined test, a test based on Graybill-Deal's estimator, an approximation to the likelihood ratio test, and some tests derived using some Bayesian considerations for improper priors along with intuitive considerations. Based on some theoretical findings and mostly based on a Monte Carlo study the conclusions are that for the most part the Bayes-intuitive type tests are superior and can be recommended. When the variances of the populations are close the approximate likelihood ratio test does best.

Original language | English (US) |
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Pages (from-to) | 207-227 |

Number of pages | 21 |

Journal | Journal of Statistical Planning and Inference |

Volume | 9 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1984 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics

## Keywords

- Admissibility
- Asymptotically Bahadur optimal
- Common mean
- Convex acceptance sections
- Hypothesis testing
- t-test