Stat 500 Midterm 1 – 2 October 2007 page 1 of 6
Please put your name on the back of your answer book.
Do NOT put it on the front. Thanks.
•The exam is closed book, closed notes. Use only the formula sheet and tables I provide today.
You may use a calculator.
•Write your answers in your blue book. Ask if you need a second (or third) blue book.
•You have 2 hours (120 minutes) to complete the exam.
Stop working when the end of the exam is announced.
•Points are indicated for each question. There are 120 total points.
•Important reminders:
–budget your time. Some parts of each question should be easy; others may be hard. Make
sure you do all parts you can.
–notice that some parts do not require any computations.
–show your work neatly so you can receive partial credit.
•Good luck!
1. 10 pts. This problem is based on a study of nurses salaries in for-profit and non-profit hospitals.
The investigators are interested in the evenness of salaries; that is whether all nurses receive
similar salaries or whether salaries are very different. The Gini coefficient was used as the
measure of salary evenness. The details of the computation are irrelevant, but it may help to
know that a Gini coefficient of 0 indicates all salaries are identical (maximum possible evenness)
and a coefficient of 1 indicates the minimum possible evenness.
The investigators randomly sampled 20 for-profit hospitals and 20 non-profit hospitals in the
United States and computed the Gini coefficient for each group. Here is what they found:
Group niGini coefficient s.e.
for-profit 20 0.672 0.120
non-profit 20 0.457 0.105
difference 0.215 0.159
The investigators computed a randomization distribution with 99 values. Here are the 10 smallest
and 10 largest values in the randomization distribution:
-0.456 -0.356 -0.273 -0.257 -0.231 -0.210 -0.198 -0.157 -0.152 -0.143 · · · 0.171 0.172 0.181 0.218
0.239 0.248 0.263 0.357 0.440 0.601
They also computed a bootstrap distribution with 100 values. Here are the 10 smallest and 10
largest values in that distribution.
-0.173 -0.171 -0.168 -0.150 -0.143 -0.141 -0.135 -0.130 -0.127 -0.113 · · · 0.554 0.555 0.568 0.599
0.608 0.642 0.717 0.745 0.786 0.800
a) 5 pts. Calculate an appropriate design-based 90% confidence interval for the difference between
the Gini coefficients between for-profit and non-profit hospitals in the United States. If you need
additional information, indicate what is needed.
b) 5 pts. Is it reasonable to extrapolate from the 40 hospitals in the study to all for-profit and
all non-profit hospitals in the United States? Briefly explain why or why not.
