A parametric hypothesis test make assumptions about the underlying distribution of the population from which the sample is being drawn, and which is being investigated. This is typically that the population conforms to a normal distribution.
Parametric hypothesis tests include:
ANOVA 
comparing the means of several (more than two) samples 
ChiSquare Test 
testing 'goodness of fit' to an assumed distribution 
Contingency Tables 
a variation on the chisquare test 
Ftest 
comparing variances 
Proportion Test 
for differences between large or small proportions 
ttest 
comparing the mean to a value, or the means of two samples 
ztest 
as ttest but for large samples 
If the underlying distribution of the population is not known then a nonparametric test would be used. This would not be as powerful because it cannot use the predictable properties of the distribution.
