Some Important Concepts

Null Hypothesis $\left( H_{0}\right)$

A maintained hypothesis that is held to be true unless sufficient evidence to the contrary is presented. This maintained claim usually carries some form of significance or importance .

Alternative Hypothesis $\left( H_{1}\right)$

A hypothesis that is held to be true when the null hypothesis is rejected.

Simple Hypothesis

A hypothesis that specifies a single value for a population parameter of interest.

Composite Hypothesis

A hypothesis that specifices a range of values for a population parameter of interest.

One-sided Alternative

An alternative hypothesis involving all possible values of a population parameter on either one side or the other of the value specified by a simple null hypothesis.

Two-sided Alternative

An alternative hypothesis involving all possible values of a population parameter other than the value specified by a simple null hypothesis.

Type I Error

The mistake of rejecting a true null hypothesis.

Type II Error

The mistake of accepting a false null hypothesis.

Significance Level $\left( \alpha \right)$

The probability of rejecting a true null hypothesis. This is usually kept at a lower value closer to zero.

Power $\left( 1-\beta \right)$

The probability of rejecting a false null hypothesis. This is determined by both the chosen $\alpha$ level and the testing procedure.

p-value / probability value

The smallest significance level at which a null hypothesis can be rejected. Alternative, one can think of it as the level of significance $\alpha$ when the evidence is used as a critical value.