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MATH 2560 3.0
Assignment 3


This is Assignment 3 for all sections. The due date will be announced in each section during class. Once all the assignments are collected, the solution will be posted on the web.


Question 1: We might expect states with more poverty to have fewer doctors. The below table gives data on the percent of each state's residents living below the poverty line and on the number of M.D.'s per 100,000 residents in each state.


  Poverty M.D.'s per   Poverty M.D.'s per
State percent 100,000 State percent 100,000
Alabama 15.1 198 Montana 15.9 190
Alaska 8.6 167 Nebraska 11.0 218
Arizona 15.2 202 Nevada 11.0 173
Arkansas 16.4 190 New Hampshire 8.9 237
California 15.3 247 New Jersey 8.5 295
Colorado 8.6 238 New Mexico 20.8 212
Connecticut 8.4 354 New York 15.7 387
Delaware 10.1 234 North Carolina 13.0 232
D.C. 19.7 737 North Dakota 13.9 222
Florida 13.3 238 Ohio 11.4 235
Georgia 13.7 211 Oklahoma 13.5 169
Hawaii 11.9 265 Oregon 13.1 225
Idaho 13.9 154 Pennsylvania 10.6 291
Illinois 10.4 260 Rhode Island 11.4 338
Indiana 8.3 195 South Carolina 12.8 207
Iowa 8.7 173 South Dakota 11.7 184
Kansas 10.5 203 Tennessee 13.2 246
Kentucky 13.8 209 Texas 15.6 203
Louisiana 18.2 246 Utah 7.9 200
Maine 10.4 223 Vermont 9.6 305
Maryland 7.6 374 Virginia 9.8 241
Massachusetts 10.9 412 Washington 9.2 235
Michigan 10.3 224 West Virginia 16.7 215
Minnesota 9.1 249 Wisconsin 8.5 227
Mississippi 16.8 163 Wyoming 11.9 171
Missouri 11.1 230      

a)
Make a scatter plot and calculate a regression line suitable for predicting M.D.'s per 100,000 from poverty rate. Draw the line on your plot.
b)
The District Columbia is an outlier, with both very many M.D.'s and a high poverty rate. (D.C. is a city rather than a state.). Circle the point for D.C. on your plot and explain why this point may strongly influence the least-squares line.
c)
Calculate the regression line for the 50 states, omitting D.C. Add the new line to your scatter plot. Was this point highly influential? Does the number of doctors now go down with increasing poverty, as we initially expected?


Question 2: The National Halothane Study was a major investigation of the safety of anesthetics used in surgery. Records of over 850,000 operations performed in 34 major hospitals showed the following death rates for four common anesthetics.

Anesthetic A B C D
Death rate 1.7% 1.7% 3.4% 1.9%
There is a clear association between the anesthetic used and the death rate of patients. Anesthetic C appears dangerous.
a)
Explain why we call the National Halothane Study an observational study rather than an experiment, even though it compared the results of using different anesthetics in actual surgery.
b)
When the study looked at other variables that are confounded with a doctor's choice of anesthetic, it found that Anesthetic C was not causing extra deaths. Suggest several variables that are mixed up with what anesthetic a patient receives.


Question 3: People who eat lots of fruits and vegetables have lower rates of colon cancer than those who eat little of these foods. Fruits and vegetables are rich in "antioxidants" such as vitamins A, C, and E. Will taking antioxidants help prevent colon cancer? A clinical trial studied this question with 864 people who were at risk of colon cancer: The subjects were divided into four groups: daily beta carotene, daily vitamins C and E, all three vitamins every day, and daily placebo. After four years, the researchers were surprised to find no significant difference in colon cancer among the groups.

a)
What are the explanatory and response variables in this experiment?
b)
Outline the design of the experiment. Use your judgment in choosing the group sizes.
c)
Assign labels to the 864 subjects and use Table B starting at line 118 to choose the first 5 subjects for the beta carotene group.
d)
The study was double-blind. What does this mean?
e)
What does "no significant difference" mean in describing the outcome of the study?
f)
Suggest some lurking variables that could explain why people who eat lots of fruits and vegetables have lower rates of colon cancer. The experiment suggests that these variables, rather than the antioxidants, may be responsible for the observed benefits of fruits and vegetables.


Question 4: At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed: what is that chance? Why is your sample not an SRS?



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Qing Shao 2002-10-20