Using t-distribution and t-test with R
A Student t-distributed random variable is modeling the ratio between a standard Normal random variate and square root of a Chi-squared random variable divided by its degrees of freedom.
A Student t-distributed random variable is modeling the ratio between a standard Normal random variate and square root of a Chi-squared random variable divided by its degrees of freedom.
In hypothesis testing, the possibility of the other side than the conclusion usually exists, and the analysis commits so-called Type I and Type II errors, with respect to the truth and the decision made upon the random sample and hypotheses. In particular, a Type I error measures the probability that a true Null hypothesis (H0) is incorrectly rejected, and a Type II error says the probability that a false H0 not being rejected, respectively.
In hypothesis testing, the analyst has chance to commit both Type I and Type II errors. The Type I error (α) refers to the probability of wrongly rejecting a true Null hypothesis – H0, while the Type II error (ß) represents the probability that failing to reject a false H0. The value of 1- ß is called the Power of Test in hypothesis testing. Its value says the ability of correctly rejecting a false H0, under the specified Null hypothesis – H0 and Alternative hypothesis – H1.
In statistical hypothesis testing, there are usually two types of errors that the process will encounter, namely Type I and type II errors. Type I error (α) refers to the probability of rejection of a Null Hypothesis (H0) when actually it is true, and if a false Null hypothesis is missed to reject when an Alternative Hypothesis (H1) is true, then a type II error (ß) occurs.