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Hypothesis testing is the use of statistics to determine the probability that a given hypothesis is true. The usual process of hypothesis testing consists of four steps. 1. ...

A hypothesis is a proposition that is consistent with known data, but has been neither verified nor shown to be false. In statistics, a hypothesis (sometimes called a ...

The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. It is usually taken to be that the observations are the ...

A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true (usually that observations are the result of chance). ...

The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers aleph_0 and the "large" ...

Let S be the set of all possibilities that satisfy hypothesis H, and let S^' be the set of all possibilities that satisfy hypothesis H^'. Then H^' is a nested hypothesis ...

Let mu(sigma) be the least upper bound of the numbers A such that |zeta(sigma+it)|t^(-A) is bounded as t->infty, where zeta(s) is the Riemann zeta function. Then the Lindelöf ...

Every dense linear order complete set without endpoints having at most omega disjoint intervals is order isomorphic to the continuum of real numbers, where omega is the set ...

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta ...

When n is an integer >=0, then J_n(z) and J_(n+m)(z) have no common zeros other than at z=0 for m an integer >=1, where J_n(z) is a Bessel function of the first kind. The ...