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?