A Marketing Study Was Conducted to Compare the Mean Age $\mathrm { n } = 10 , \quad$

A marketing study was conducted to compare the mean age of male and female purchasers of a certain product. Random and independent samples were selected for both male and female purchasers of the product. It was desired to test to determine if the mean age of all female purchasers exceeds the mean age of all male purchasers. The sample data is shown here:

Female: $\mathrm { n } = 10 , \quad$ sample mean $= 50.30 , \quad$ sample standard deviation $= 13.215$
Male: $\mathrm { n } = 10 , \quad$ sample mean $= 39.80 , \quad$ sample standard deviation $= 10.040$

Which of the following assumptions must be true in order for the pooled test of hypothesis to be valid?
I. Both the male and female populations of ages must possess approximately normal probability distributions.
II. Both the male and female populations of ages must possess population variances that are equal.
III. Both samples of ages must have been randomly and independently selected from their respective populations.

A) I only
B) III only
C) II only
D) I, II, and III