What type of association would you expect between a person's age and hair length?

The length of their hair reduces. This is because the length of hair is dependent on the growth phase (anagen phase) of the hair follicles. When one is young, the cells of the papilla divide more rapidly and hence cause the length of the hair to be long before reaching transitional phase (catagen phase) and then shed off in the telogen phase. The older one gets, the papilla cells do not divide as rapidly and the length of the hair shortens with age.

this is true, assuming that the allele is completely recessive and incomplete dominance is not a factor.