RETRACTED: The probable error in the hypothesis test of normal means using a small sample (Retracted Article)

In a small-sample hypothesis testing(s) of mean(s) from a normal population(s), the degrees of freedom is equal to the divisor in the formula of the sample standard deviation. In this paper, it is shown that the commonly used divisors are smaller than the correct divisors in hypothesis tests of one mean, two means and three means from a normal population(s), new methods are proposed, which provide an improved power in those hypothesis testings. Extension to cases for more than three means are straightforward from the presentations in this paper. Understanding this can be beneficial to practitioners and students of Statistics.