Editing Interval estimation (section)

== One-sided vs. two-sided ==
[[File:Confidence Interval Differentiation.png|thumb|Differentiating between two-sided and one-sided intervals on a standard normal distribution curve.]]
Two-sided intervals estimate a parameter of interest, Θ, with a level of confidence, γ, using a lower (<math>l_b</math>) and upper bound (<math>u_b</math>). Examples may include estimating the average height of males in a geographic region or lengths of a particular desk made by a manufacturer. These cases tend to estimate the central value of a parameter. Typically, this is presented in a form similar to the equation below.

:<math>P(l_b < \Theta < u_b) = \gamma</math>

Differentiating from the two-sided interval, the one-sided interval utilizes a level of confidence, γ, to construct a minimum or maximum bound which predicts the parameter of interest to γ*100% probability. Typically, a one-sided interval is required when the estimate's minimum or maximum bound is not of interest. When concerned about the minimum predicted value of Θ, one is no longer required to find an upper bounds of the estimate, leading to a form reduced form of the two-sided.

:<math>P(l_b < \Theta) = \gamma</math>

As a result of removing the upper bound and maintaining the confidence, the lower-bound (<math>l_b</math>) will increase. Likewise, when concerned with finding only an upper bound of a parameter's estimate, the upper bound will decrease. A one-sided interval is a commonly found in material production's [[quality assurance]], where an expected value of a material's strength, Θ, must be above a certain minimum value (<math>l_b</math>) with some confidence (100γ%). In this case, the manufacturer is not concerned with producing a product that is too strong, there is no upper-bound (<math>u_b</math>).