STAT 557
Fall 2000
EXAM II
Name ____________
Instructions: This is a take home exam. You can use any computer software, books or other
materials of your choice. This should be your own work, however. You should
not discuss this exam with any other person, except Dr. Koehler and Xiao-Hu Liu.
Contact Dr. Koehler or Xiao-Hu Liu if you have problems with statistical
computations. Contact Dr. Koehler if you have other questions about this exam.
There are two problems on this exam. Each requires an analysis of some data.
Keep your answers as concise as possible. You may include graphs or selected
tables of computer output, but do not attach unedited computer output. Your
answers need not be typed, but write as neatly as possible.
The answer for each problem should be presented in the following format, and in
the following order.
1.
Summary paragraph. In a few sentences, report your major findings or
results of practical importance. Use sentences such as “Demand for
medical services is greater among people covered by government
programs than among people covered by private insurance plans.” Write
for business managers or a general scientific audience. Do not use
formulas or technical statistical jargon.
2.
Brief description of model development.
Give a brief summary of the steps you took to select models and methods
of analysis. No tests of significance or computer output are needed here.
Do not report formulas for models you did not select. Just write a
paragraph describing what you considered and the decisions you made in
selecting models and methods of analysis.
3.
Report the formula for your final model and/or your other results.
You should include a list of parameter estimates and their standard errors.
You can include computer-generated output to do this. Interpret your final
model and your other results of your analysis with respect to the context of
the problem. State your conclusions.
4.
Provide support for your model or your choice of analyses.
Convince me that your final model or methods of analysis are appropriate
for the data. Present supporting evidence. In this part you can also
comment on other models or analyses that would be worthwhile to
investigate, if you had more time, but explain why such additional
investigation would be worthwhile.
Do not forget to put your name on your solutions to this exam. Keep your
answers concise and focused. You will lose credit for including
inappropriate analyses or irrelevant information. If you turn in more than
one solution for a problem, you will only receive credit for the weakest of
your solutions.
2
PROBLEM 1:
The data for this problem were taken from a simple random sample of unmarried adults in
Australia. The counts for a 2x6x3x2x2x2x2 contingency table are stored in the file
exam2p1.dat that is available from the course web page. SAS and S-PLUS software for
reading this file are stored in the files exam2p1.sas and exam2p1.ssc, respectively. There
are eight numbers on each line of the file in the following order.
Sex:
1 = female
Age Group:
1
2
3
4
5
6
=
=
=
=
=
=
Health Insurance:
1
2
= covered by government insurance
= covered by private insurance
Illness:
1 = at least one illness in the last two weeks
2 = no illness in the last two weeks
Chronic Conditions:
1 = at least one condition that requires long term medical care
2 = none
Doctor Visits:
1 = consulted with a doctor in the last two weeks
2 = did not see a doctor in the last two weeks
Other Health Care:
1
2
Count:
2 = male
20-29 years old
30-39 years old
40-49 years old
50-59 years old
60-69 years old
at least 70 years old
= at least one visit in the last two weeks with a non-doctor
health professional (optician, physiotherapist, community nurse,
chiropractor, social worker, pharmacist, etc….
= no such visit in the last two weeks
The number of respondents
This study was concerned with the associations between demand for health care services, in
this case doctor visits and visits with other health care professionals, and coverage with
government or private health insurance programs. For example is there more demand for a
certain kind of service from those covered by government insurance than by those covered
by private insurance. The age and sex of the respondents are demographic variables that
may be related to demand for health care and the type of health insurance coverage.
Respondents were asked to report on their use of health care services in the last two weeks.
Consequently, they were also asked to report illnesses experienced in the last two weeks.
Chronic illnesses are ongoing illnesses that require regular long-term care.
Analyze these data and describe associations among variables. Give special attention to the
issue of whether or not government and private insurance plans are associated with the same
level of demand for health care among unmarried adults in Australia.
3
PROBLEM 2:
For certain species of turtles, the sex of hatchlings is largely determined by the temperature
at which the eggs are incubated. To examine the effect of incubation temperature, samples
of newly laid eggs were collected in Iowa for each of two species of turtles, called species A
and species B. The eggs were taken to a laboratory and incubated at specific temperatures.
A randomized assignment of eggs to incubation temperatures was employed for each
species. The numbers of females and males that emerged from the eggs was recorded at
each temperature for each species. The experiment was repeated with samples of newly laid
turtle eggs collected in Louisiana for the same two species of turtles.
The data are stored in the file exam2p2.dat that is available from the course web page.
There are six columns of numbers in this file corresponding to the following variables in the
order listed.
Temperature:
Incubation temperature (ºC)
Species:
Coded 1 or 2
Location:
1 = Iowa
Females:
Number of female turtles that hatched
from eggs collected in this location
and incubated at this temperature
Males:
Number of male turtles that hatched
from eggs collected in this location
and incubated at this temperature
Total:
Number of eggs collected in this
location that were incubated at this
temperature
2 = Louisiana
Analyze these data. Describe how the conditional probability that a male turtle hatches
from a randomly selected egg is related to temperature, location, and species.