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{\LARGE
Statistics \hfill Class Project --- Part 1 of 3 \\
}
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This is the first part of the three-part class project. The class
project is designed to give you a longitudinal perspective of the
topics covered in the course. The grading for the course project will
be 80\% correctness, 20\% clarity of presentation. I encourage you to 
{\it neatly} write up your answers, as you
will be using them in the future parts of the project.

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\noindent{\LARGE 1. DATA COLLECTION}

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(a) Flip a coin 120 times. Record the results of this experiment 
in 5 rows, with 24 flips per row. For example, the first row may be

\begin{center}
H T H T T T H T T H T T H H H T T H T H H H H T
\end{center}

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(b) For each {\it pair} of flips, write down the number of heads
in that pair. For the 24 flips shown above, this would be done as 
follows:

\begin{displaymath}
\underbrace{\hbox{H T}}_1 \;
\underbrace{\hbox{H T}}_1 \;
\underbrace{\hbox{T T}}_0 \;
\underbrace{\hbox{H T}}_1 \;
\underbrace{\hbox{T H}}_1 \;
\underbrace{\hbox{T T}}_0 \;
\underbrace{\hbox{H H}}_2 \;
\underbrace{\hbox{H T}}_1 \;
\underbrace{\hbox{T H}}_1 \;
\underbrace{\hbox{T H}}_1 \;
\underbrace{\hbox{H H}}_2 \;
\underbrace{\hbox{H T}}_1 
\end{displaymath}

The numbers would then be separately recorded into a data set. 
You should {\it explicitly} show underbraces in your write-up.
The result will be a data set with 60 numbers --- each either 0, 1, 
or 2.  We will refer to this as Data Set A.

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(c) Repeat (b), except for each {\it triple} of flips. For the 24 flips
shown above, the result would be

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2~~~0~~~1~~~1~~~3~~~1~~~2~~~2
\end{center}

The full data set will have 40 numbers --- each either 0, 1, 2, or 3.
We will refer to this as Data Set B.

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\noindent{\LARGE 2. DATA PRESENTATION}

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(a) For Data Set A, make a {\it frequency table} displaying how often 
each pair had 0, 1, and 2 heads. 

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(b) For Data Set B, make a {\it frequency table} displaying how often
each triple had 0, 1, 2, and 3 heads.

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(c) Using these frequency tables, draw {\it relative-frequency histograms}
for both Data Sets A and B. Use 3 classes for Data Set A and 4 classes
for Data Set B. \underline{Important}: Since the class width is 1
for both data sets, you don't need to worry about class limits and class
boundaries for this problem --- that is, the production of these histograms
will be somewhat easier than the examples from the book and from class.
For Data Set A, just draw rectangles of appropriate height and width 1 over 
0, 1, and 2. For Data Set B, draw rectangles of width 1 over 0, 1, 2, and 3.

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(d) {\it Without doing any calculations}, draw a rough picture of what
you think the relative-frequency histogram for groups of {\it four} flips
may look like. Briefly justify your picture.

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\noindent{\LARGE 3. DATA ANALYSIS}

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Compute the sample mean ($\overline{x}$) and sample standard deviation ($s$)
for Data Sets A and B. You should select (and mention) the method you 
used to compute these descriptive statistics most efficiently.
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