\documentclass[12pt,titlepage]{article}
\usepackage{amsmath}
\usepackage{graphicx}
\allowdisplaybreaks

\jot=.2in \pagestyle{plain} \setlength{\topmargin}{-.5in}
% \setlength{\footheight}{0 in}
\setlength{\textheight}{9.5in}
\setlength{\oddsidemargin}{-0.2in}
\setlength{\evensidemargin}{-0.1in}
\setlength{\textwidth}{6.8in}
\font\heada=cmbx10 scaled\magstep3
\font\headb=cmsl10 scaled\magstep1
\font\headc=cmr8
\pretolerance=10000
\setlength{\parindent}{2 em}

\begin{document}
\begin{center}
{\heada Project 8 - Hypothesis Testing using two samples}\\
{\headb Statistics 401: Fall 2006}\\
{\it Due Wednesday, April 18}
\end{center}
\bigskip

\noindent Turn in your answers in a type-written report.  For each
hypothesis test performed, show all SIX steps of the test and give
all relevant work and answers in the body of your report.  Give all
R-output in an appendix.


\begin{enumerate}
\item In a study of middle aged Finnish men (see the abstract for
{\em Coffee Drinking Is Dose-Dependently Related to the Risk of
Acute Coronary Events in Middle-Aged Men} from the September 2004
Journal of Nutritional Epidemiology, available at the STAT401 web
page), the researchers were interested in determining if there is a
relationship between coffee consumption and white blood cell count
(white blood cells or {\em leukocytes} defend the body against
infection and disease by ingesting foreign materials and cellular
debris, by destroying infectious agents and cancer cells, or by
producing antibodies).  The white blood cell count of $n_1=77$
non-coffee drinkers was compared to $n_2=351$ heavy coffee drinkers
(those who drink on average 950 ml of coffee each day). The study
reported that $\bar x_1=5.2$, $s_1=1.4$, $\bar x_2=6.0$, and
$s_2=1.7$. These white blood cell counts are in billions per liter.

\begin{enumerate}
\item How many 8oz cups of coffee does 950ml correspond to?  Does
this make you a heavy coffee drinker?

\item Explain why a pooled procedure (instead of an un-pooled) is appropriate to analyze
these data?   Explain.

\item Find a 99\% confidence interval for the mean difference in white blood cells
between non-coffee drinkers and heavy coffee drinkers.  Use a pooled
procedure.

\item Be sure to check your assumptions!

\item Give a conclusion in terms of the problem.

\item Can we conclude that drinking coffee causes middle aged men to
have higher white blood cell counts?   Why or why not?

\item The study was really interested in determining the effects of coffee consumption
on coronary heart disease.
In light of your answer to the previous question, comment on
the assertion in the abstract that ``heavy coffee consumption
increases the short-term risk of acute myocardial infarction or
coronary death."

\end{enumerate}



\item Read the article ``The upside of color blindness" in the
April 2007 issue of {\em Discover} available at the STAT401 web
page.   A hypothetical data set for the 34 capuchins who took part
in the study is also at the web site.
\begin{enumerate}
\item Explain why an un-pooled procedure (instead of a pooled) is preferred to analyze
these data.

\item Perform an un-pooled test BY HAND.  Use a significance level of
$\alpha=.05$.   Show the six steps in your report.  Be sure to
indicate what assumptions you must make.  Use the exact degrees of
freedom using the appropriate formula.  Check your assumptions!

\item Use R's t.test function to verify the results of your test.
Include the R-code and R-output in the Appendix of your report.
\end{enumerate}


\newpage
\item Do problem 11.32 on pages 485-6 of your textbook.
\begin{enumerate}
\item Perform the test BY HAND at a significance level of $\alpha=.05$.

\item Use R's t.test function to verify the results of your test.
Include the R-code and R-output in the Appendix of your report.
\end{enumerate}


\item According to the Center for Disease Control (CDC), 76 million people in the US get diarrhea and
upset stomachs each year. Most of these infections can be prevented
by regularly washing one's hands.  A microbiologist believes that
more women than men wash their hands after using the bathroom.  From
a SRS of 132 men, 33 admit to washing their hands.   From a SRS of
109 women, 93 admit to washing their hands (These values for each
gender are consistent with those reported by the CDC).

\begin{enumerate}
\item \label{CDChyp}  Give the hypotheses whose alternative hypothesis reflects the microbiologist's belief.

\item Calculate a 99\% CI for the difference of proportions BY
HAND.

\item What is your conclusion in terms of the problem?

\item With respect to the hypotheses from from \eqref{CDChyp}, does your conclusion lead you to reject ${\rm H}_0$ in favor of ${\rm H}_a$?   Why or why not?

\item Check your answers by using R's prop.test function, and include
the R-code and R-output in an Appendix.
\end{enumerate}


\item Regarding the AP article {\em Bad News For Male Mountain Bikers} available through the STAT401 web site, answer the following:

\begin{enumerate}

\item Give the set of hypotheses which should be tested to
determine if a higher proportion of male ``extreme" mountain bike
riders have low sperm counts and scrotal abnormalities when compared
to other males.

\item Perform the rest of the hypothesis test by hand, being sure to check your
assumptions!   Even if the assumptions are not satisfied, conduct
the test.

\item Even if the assumptions for the test you just performed were met, could the results of this study
be used to justify the assertion:

\begin{verse}
\noindent Frequent mountain biking may reduce fertility in men,
according to a small Austrian study  ... The research suggests
frequent jolts and vibration caused by biking over rough terrain may
cause abnormalities, including small scars within the scrotum and
impaired sperm production.
\end{verse}

Why or why not?

\item Check your answers using R's prop.test function, and include the R-code and R-output in the Appendix of
your report.
\end{enumerate}

\end{enumerate}


\end{document}