Math A-lympiad: Final 1995-1996

Predicting the number of university students in the Netherlands 

Introduction
In recent years there were a lot of changes in the number of first year (or: entering) university students at Dutch universities. Beside changes in the total number of students, also a number of shifts can be seen, for instance: shifts between technical studies and social studies, as well as shifts between different universities. Further, the popularity of specific studies has hanged over time.

For the Dutch universities as well as for the Dutch politics it is important to know why these changes in the numbers of students and the shifts between studies and universities occur, and what to expect in the near future. It can easily be understood that demographic factors - these are factors that concern population-growth and populationstructure, like families having fewer children and people getting children at a later age -, have a strong impact. Also, the fact that it is nearly impossible to get a good job based on a high school {secondary school, age 12-18} degree only, is an important factor. Furthermore, polital decisions on economizing on scholarships and number of years, allowed to study, will cause difficulties in going from HBO to university.  Finally, all kinds of economical developments, particularly concerning employment, like the closing of business and industry, have an effect on the choices future students make.

Data
In the appendices you will find large numbers of data. Most of these are taken from the 1995 yearbook of Statistics, a publication from the Dutch central bureau of statistics. You will have to decide for yourselves which of these data are useful when answering the questions and how these data can best be used and combined.

Task
The Union of Cooperating Dutch Universities (UCDU) has asked your team to write a report, in which predictions will be made on numbers of first year students for the next 5 years.
The report should contain an elaboration of the following parts (devote at least one "chapter" of the report on each part):

  1. Based on the data, make an estimation for the total number of first year students to be expected to enter all Dutch universities together in september 1995 up to and including 1999.
  2. Investigate which shifts have occured in the last five years between student numbers over the different categories of studies Agriculture, Physical sciences, Technical sciences, Health, Economics, Law, Social studies, Language and culture and try to explain those shifts. Predict how the first year students of 1995 up to and including 1999 will be distributed among those categories of studies.
  3. The UCDU is also interested in knowing how many first year students will enter each of the universities the next five years. Find a method to predict these numbers. Just a limited number of data is available on this subject; indicate which data possibly could have been useful, to come to a good prediction of the number of first year students.

    4. You might illustrate your method, using the information that is available on the University of Groningen.
Don't forget to include your 'way of working', what data you used, what assumptions you made, your approach or line of reasoning, and try to say something about the reliability of the predictions.