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\centerline{MONT 106N -- Identifying Patterns}
\centerline{Information and Sample Questions for Midterm 1}
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\noindent
{\it General Information}
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The first midterm exam will be given in class on Monday, October    
19.  It will cover the material from Chapters 1 - 7 of Freedman,
Pisani, Purves.  This means in particular:
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\item{1.}  Issues about the design of studies -- controlled experiments
versus observational studies, questions like the ones from Problem Set
1 about whether conclusions are justified, possible confounding factors,
and so forth.  A question here might ask for a paragraph-length written
response rather than just a calculation.
\item{2.}  Histograms -- be able to construct histograms for 
``small'' data sets, explain the conceptual meaning of the histogram, etc.
\item{3.}  Averages, medians, and standard deviations -- be able to compute
these for ``small'' data sets by hand.  Also be prepared for 
conceptual questions about what these measures tell us about data.
\item{4.}  Normal approximation to data -- using the normal curve
and the normal curve area table (questions similar to Problem Set 3), percentiles, etc.

\item{5.}  Equations of lines in the plane.
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\noindent
No use of cell phones, pagers, I-pods, or any other electronic devices
beyond a calculator will be allowed during the exam -- turn them off
and stow them in your backpack.
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\noindent
{\it Important Note:}  I will be out of town starting from about
noon on Wednesday, October 14, until the middle of the day on 
Sunday, October 18.  I will have office hours on Wednesday
morning and I will be in email contact, though.
So if you have questions as you prepare, I will try to respond
as soon as possible. 
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\noindent
{\it Sample Exam Questions}
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Be sure to provide explanations for your answers if that is asked for.
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\noindent
I.  
\item{A)}  What is a {\it confounding factor}?  What are the techniques
used in well-designed controlled experiments to try to minimize their effects?  
\item{B)}  Here is a passage from Dr. Dean Edell's column in the San Francisco
Chronicle of August 1, 1990:  
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\item{}
{\it ``The more experienced a doctor is, the better.
As obvious as that sounds, there are still too many people out there who never 
ask surgeons for a history of their work.  The importance of knowing this is 
illustrated by this study.  Peter Starek, a surgeon at the University of 
North Carolina, reviewed 460 heart valve replacement operations and found
that only $4\%$ of the patients of the three most senior surgeons died.
But one junior surgeon lost almost $33\%$ of his patients.  Since that
surgeon was technically the best in the group, says Starek, something
was obviously lacking -- perhaps the kind of good judgment that grows
out of experience...''}
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\itemitem{1.}  Was Starek's study a controlled experiment or an
observational study?
\itemitem{2.}  Is Starek's claim justified by this evidence?  Or
are there possible confounding factors he is overlooking?
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\noindent
II.
\item{A)}  Find the equation of the line passing through the 
points $P = (2,6)$ and $Q = (-5,2)$ in the plane.
\item{B)}  Find the equation of the line perpendicular to the 
line in part A and passing through the origin $O = (0,0)$.
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\noindent
III. The following data on people without health insurance by family income level
for 2006 is from the Current Population Survey.
$$\matrix{ & {\rm Family\ Income} & {\rm No\ Insurance} & {\rm All\ People} & \cr
           &                      &     N = 44,815  &    N=293,834 &\cr
           & {\rm Less\ than\ } \$25,000 &  18,590 & 70,478 \cr
           & \$25,000 {\rm\ to\ } \$49,999    & 13,620  & 72,963\cr
           & \$50,000 {\rm\ to\ } \$74,999    &  6,445  & 55,258\cr
           & \$75,000 {\rm\ to\ } \$200,000   &  6,160  & 95,136\cr}$$
Notice $N=$ at the top of each column is the total number of people in the four class
intervals for the column. Also, the number of people is in units of 1000.
\item{1.} For each of the four income class intervals, compute the percentage of No Insur-
         ance people in the class interval and the percentage of all people in the interval.
\item{2.} Use your percentages from 1. to construct two histograms, one for people without
         insurance and one for all people using the class intervals in the table. (Use the
         graph paper.)
\item{3.} By comparing your histograms, what can you say about the distribution of people
         without health insurance by family income in comparison to the distribution of
         all people by family income?
\item{4.}  Is the average income or the median income larger for the families
with no insurance?  Explain how you can tell.
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\noindent
IV. The grades in a large university statistics class are normally distributed
with a mean of 60 (out of a possible 100 points) and an SD of 12.
\item{1.} Draw a smooth histogram for the data.
\item{2.} If 200 students took the test, estimate how many scored between 70 and 80.
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\noindent
V. (Hypothetical) A big town near Worcester administers a spelling test to all
   students in fourth grade. The test consists of 100 words.
   The average for the number of words correctly spelled
   was 50 with a standard deviation of 10.  Suppose a student was in the 70th percentile.
   What would you estimate for the number of words the student spelled correctly? 
   (Be sure to show your calculations and draw normal approximations as needed.)
\bye
