hypothesis testing; Fisher information matrix; concentration of the statistical population in prescribed tolerance limits; statistical quality control; normal distribution; explicit formulas for critical regions; finite sample sizes; fourth moment
In the paper a test of the hypothesis $\mu+c \sigma \leq M$, $\mu - c \sigma \geq m$ on parameters of the normal distribution is presented, and explicit formulas for critical regions are derived for finite sample sizes. Asymptotic null distribution of the test statistic is investigated under the assumption, that the true distribution possesses the fourth moment.
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