# For example, using Z-test of hypothesis in the following Figure.

Construction of confidence interval for , variance unknown **Example:** Given xbar_{16} = 12.1, S^{} = 2.225 develop a 95% confidence interval for Therefore P[11.31 ] 0.95 Again, notice the **Duality** between the test of hypothesis and confidence interval.

## Consistent with this hypothesis, the specific ..

### Version space learning - Wikipedia

From a deductive-logical point of view, the set of logicalconsequences of a given state description is a maximal consistent setof sentences of *L*(3): The set is consistent (consisting as itdoes of the logical consequences of a consistent sentence) andmaximal; no sentence of *L*(3) not implied by the set isconsistent with it. The state descriptions correspond to models, topoints in a logical space. A (symmetrical) probability on *L*(3)thus induces a normal measure on sets of models: Any assignment ofnon-negative numbers summing to one to the state descriptions ormodels fixes probabilities. In this finite case, the extent to whichevidence *e* supports a hypothesis *h* is the proportionof models for *e* in which *h* istrue. Deductively, *e* logically implies *h*if *h* is true in every model for *e*. Degree ofconfirmation is thus a metrical generalization of first-order logicalimplication.

### Version space learning is a logical approach to machine ..

A very different approach is based on the idea that disproof need notbe demonstrative. The goal of this approach is to show that theexistence of an omni-God is so improbable that confident belief in thenon-existence of such a God is justified. Two such arguments arediscussed in detail below: the “low priors argument” andthe “decisive evidence argument”. Each of these argumentsemploys the same specific strategy, which is to argue that somealternative hypothesis to omni-theism is many times more probable thanomni-theism. This doesn’t imply that the alternative hypothesisis probably true, but it does imply that omni-theism is very probablyfalse. In the case of the second argument, the alternative hypothesis(aesthetic deism) is arguably a form of theism, and even in the caseof the first argument it is arguable that the alternative hypothesis(source physicalism) is compatible with some forms of theism (inparticular ones in which God is an emergent entity). This is not aproblem for either argument, however, precisely because both arearguments for local atheism instead of global atheism.

## A possible definition of machine leaning is ..

Progol reduces this combinatorial explosion by using an alternative approach, called mode directed inverse entailment (MDIE). Inverse entailment is used to generate the most specific *h* that, together with background information, entails some observed data. General-to-specific search is then performed through a hypothesis space H bounded by the most specific hypothesis and constrained by the user-specified predicates.