In this paper, some new exact tests and
confidence intervals of variance components in nested error
component regression model with three random effects are developed
by using generalized p-value and generalized confidence interval.
Invariance of these tests and confidence intervals under scale
transformation is also discussed. It is showed that the generalized
p-value is feasible and effective to resolve the hypothesis
testing problems with nuisance parameters. A simulation study is
conducted to illustrate the powers of these tests and coverage
probabilities.