Hypothesis testing and confidence intervals concerning one or two means

Abstract

In this chapter, the continuous variate X under study will be assumed to follow a normal probability distribution (chapter 5) of which the mean is μ_x and the variance σ ²_x : X ← N (µ_x,σ ²_x ). However, the methods discussed here will retain their validity in many other cases where the variate X is not normally distributed but can be transformed into another variate Y=g(X) having a normal distribution N (µ_y,σ ²_x ). In such cases, once the statistical analysis of the transformed variate Y has been completed through methods based on normal theory, results can be reexpressed with respect to the original (untransformed) variate X by using the inverse transformation X=g^-1(Y). For instance, if the original variate X follows a lognormal distribution (chapter 14), the transformed variate Y=log_e(X) has a normal distribution and the results of the statistical analysis of Y can be reexpressed with respect to X thanks to the transformation X=exp(Y).