A researcher wants to prove that there is a difference in the average age of onset of a certain disease for men and women who get the disease.

A random sample of 30 women with the disease showed an average age of onset of 83 years, with a sample standard deviation of 11 years. A random sample of 20 men with the disease showed an average age of onset of 77 years, with a sample standard deviation of 4 years.

Assume that ages at onset of this disease are normally distributed for each gender, and that they are independent of each other