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Main article: Interval estimation
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: the red line is true value for the mean in this example, the blue lines are random confidence intervals for 100 realizations.

Most studies only sample part of a population, so results don't fully represent the whole population. Any estimates obtained from the sample only approximate the population value. Confidence intervals allow statisticians to express how closely the sample estimate matches the true value in the whole population. Often they are expressed as 95% confidence intervals. Formally, a 95% confidence interval for a value is a range where, if the sampling and analysis were repeated under the same conditions (yielding a different dataset), the interval would include the true (population) value in 95% of all possible cases. This does not imply that the probability that the true value is in the confidence interval is 95%. From the frequentist perspective, such a claim does not even make sense, as the true value is not a random variable . Either the true value is or is not within the given interval. However, it is true that, before any data are sampled and given a plan for how to construct the confidence interval, the probability is 95% that the yet-to-be-calculated interval will cover the true value: at this point, the limits of the interval are yet-to-be-observed random variables . One approach that does yield an interval that can be interpreted as having a given probability of containing the true value is to use a credible interval from Bayesian statistics : this approach depends on a different way of interpreting what is meant by "probability" , that is as a Bayesian probability .

In principle confidence intervals can be symmetrical or asymmetrical. An interval can be asymmetrical because it works as lower or upper bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical because the two sided interval is built violating symmetry around the estimate. Sometimes the bounds for a confidence interval are reached asymptotically and these are used to approximate the true bounds.

Main article: Statistical significance

Statistics rarely give a simple Yes/No type answer to the question under analysis. Interpretation often comes down to the level of statistical significance applied to the numbers and often refers to the probability of a value accurately rejecting the null hypothesis (sometimes referred to as the p-value ).

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The following subsections are ordered from simple actions to more elaborate or rarer actions.

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2.5.Recipients of previous unlawful aid


3.1.Rescue aid


3.1.2.Simplified procedure

3.2.Restructuring aid

3.2.1.Basic principle

3.2.2.Conditions for the authorisation of aid

Eligibility of the firm

Restoration of long-term viability

Avoidance of undue distortions of competition

Aid limited to the minimum: real contribution, free of aid

Specific conditions attached to the authorisation of aid

Full implementation of restructuring plan and observance of conditions

Monitoring and annual report

3.2.3.Amendment of the restructuring plan

3.2.4.Restructuring aid in assisted areas

3.2.5.Aid for restructuring SMEs

3.2.6.Aid to cover the social costs of restructuring

3.2.7.Need to inform the Commission of any aid granted to the recipient firm during the restructuring period

3.3.‘One time, last time’


4.1.General principles


4.3.Conditions for the authorisation of rescue aid schemes

4.4.Conditions for the authorisation of restructuring aid schemes

4.5.Common conditions for the authorisation of rescue and/or restructuring aid schemes

4.6.Monitoring and annual reports


5.1.Compensatory measures

5.2.Definition of excess capacity

5.3.Eligibility for rescue and restructuring aid schemes

5.4.Capacity reductions

5.5.‘One time, last time’ condition

5.6.Monitoring and annual report



( 1 ) OJ C368,23.12.1994, p.12 .

( 2 ) OJ C283,19.9.1997, p.2 . See also the footnote relating to the heading of Chapter5.

( 3 ) OJ C288,9.10.1999, p.2 .

( 4 ) This refers in particular to the types of company mentioned in the first subparagraph of Article1(1) of Council Directive78/660/EEC ( OJ L222,14.8.1978, p.11 ) as last amended by Directive2003/51/EC of the European Parliament and of the Council ( OJ L178,17.7.2003, p.16 ).

( 5 ) By analogy with the provisions of Article17of Council Directive77/91/EEC ( Sale Countdown Package Outlet Locations Cheap Price Cupro Skirt DAY OF THE DEAD by VIDA VIDA Sale 2018 New Clearance Excellent Cheap Geniue Stockist cX2zV
) as last amended by the2003Act of Accession.

There are four quantities that describe concentration:

Main article: Mass concentration (chemistry)

The mass concentration ρ i {\displaystyle \rho _{i}} is defined as the of a constituent m i {\displaystyle m_{i}} divided by the volume of the mixture V {\displaystyle V} :

The SI unit is kg/m 3 (equal to g/L).

Main article: Molar concentration

The molar concentration c i {\displaystyle c_{i}} is defined as the amount of a constituent n i {\displaystyle n_{i}} (in moles) divided by the volume of the mixture V {\displaystyle V} :

The SI unit is mol/m 3 . However, more commonly the unit mol/L (= mol/dm 3 ) is used.

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The number concentration C i {\displaystyle C_{i}} is defined as the number of entities of a constituent N i {\displaystyle N_{i}} in a mixture divided by the volume of the mixture V {\displaystyle V} :

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