Appendix A.1: Background on Basic Test Statistics

Background on Basic Test StatisticsWe indicate that Y is a random variable that follows a normal distribution with mean μ and variance σ 2 by Υ~Ν(μ, σ 2 ) Central Distributions1. Let Y u Y2,•., Y n be independent normally distributed random variables with E(Y¡) = jU/, and Var(T¿) = σ,• 2 .Let a^ a 2 ,..., a n be known constants.If we define the linear combination of the 7/s by U~N [Y^a^Y^aWThe key point is that linear combinations of normally distributed random variables also follow normal distributions. If Υ~Ν(μ, σ\ thenwhere Z is the standard normal random variable.