Two and one sided tests 

A two-sided test concerning a population is a hypothesis test that is applied when we want to compare an estimate of a parameter to a given value against the alternative hypothesis not equal to the stated value.

For two samples with p₁ and p₂ this translates to:

In a two-sided test, the rejection region is divided into two parts, the left and the right sides of the considered parameter. The acceptance region lies within p₀-I,p₀+I 

A one-sided or a one-tailed test on a population(s) parameter(s) is a type of hypothesis test in which the values for which we can reject the null hypothesis, is locatwd entirely in one tail of the probability distribution (left or right). For one sided test the null hypothesis is of the form:

For two samples with p₁ and p₂ this translates to:

In a one-sided test, the rejection region is either left (right tailed) OR right (left tailed) side of the considered parameter and the acceptance region(s) are respectively (-inf,p₀-I], and [p₀+I,inf).