From Graybill and Iyer 1994,  p 486

An investigator wants to study how the salaries of high school 
teachers who teach in the public school system of a large city are 
related to experience (in years employed) and determine what the 
differences are, if any, between the salaries of male teachers and 
female teachers.

A simple random sample of male teachers and a 
simple random sample of female teachers are chosen, and their 
monthly salaries Y and years of experience X are recorded.

The 
data for both males and females are given in salaries.dat.

The study populations of items in this problem are all male
teachers  in this school system and all female teachers in the
school system, respectively, the year that the sample was 
collected. These are also the target populations of items for
this problem.

Suppose that assumptions (A) are valid for each population (male 
and female). The population regression functions for males and 
females are 

females: mu(F) | x  = a[F] + B[F].x
males:   mu(M) | x  = a[M] + B[M].x


a  Plot the estimated regression lines for both males and females 
   on the same graph.

b  What is the difference between the average salaries for males 
   and females with the same number of years of experience? Express 
   your answer in terms of population parameters.

c  What is the difference between the average starting salaries of 
   males and females? Express your answer in terms of population 
   parameters. Find a point estimate and a 95% confidence interval 
   for this quantity.

d  What population parameters would you examine to determine 
   whether the disparity between male and female salaries remains 
   constant at every experience level (years) or whether it changes 
   with years of experience for the years from O to 30 (i.e., 0 < x 
   < 30)? Find a 95% confidence interval for this quantity. 
   Explain.

e  What population parameters would you examine to determine 
   whether the salaries ever become equal in the range O < x < 30? 
   Explain.

f  The investigator will conclude that there is evidence of a 
   systematic salary differential if the difference between the 
   male and female average annual salaries exceeds $500 anywhere in 
   the range 0 < x < 30.

  i  Write the population parameters needed to determine whether 
     there is a systematic salary differential between males and 
     females.

  ii Do the data provide evidence of a systematic salary 
     differential between males and females (i.e., estimate the 
     quantities in (i))? If so, in which direction?

 iii Compute appropriate 95% simultaneous confidence intervals to
     help arrive at a conclusion in (i).