One sample t-Test

Comparison of sample mean with population mean when standard deviation of the population is estimated from the sample.

Requirements:

Dependent variable is at least interval scaled and stems from a normal distributed population.

Hypothesis:

Nondirectional:                                       Directional (example):

H0:                           H0:    or  

H1:                            H1:    or  

The term   is t-distributed with n-1 degrees of freedom.

whereas

and

The obtained t-value is then compared with the critical t-value to make the decision of significance.

However, for sufficient large samples (n > 100)* one can compute the z-Value even if is estimated from the sample:

* for large samples (n > 100) the t-distribution approximates the standard normal distribution sufficiently well.