\documentclass[11pt,titlepage]{article} \usepackage{amsmath} \usepackage{graphicx} \usepackage{verbatim} \allowdisplaybreaks \jot=.2in \pagestyle{empty} \setlength{\topmargin}{-0.6in} \setlength{\textheight}{9.5in} \setlength{\oddsidemargin}{-0.2in} \setlength{\evensidemargin}{-0.2in} \setlength{\textwidth}{6.9in} \font\heada=cmbx10 scaled\magstep3 \font\headb=cmsl10 scaled\magstep1 \font\headc=cmr8 \pretolerance=10000 \setlength{\parindent}{2 em} %\input macros \newdimen\digitwidth \newdimen\minuswidth \setbox0=\hbox{\rm0} \digitwidth=\wd0 \setbox1=\hbox{$-$} \minuswidth=\wd1 \newdimen\starr \setbox2=\hbox{${}^*$} \starr=\wd2 {\catcode`?=\active \def?{\kern\digitwidth} \catcode`@=\active \def@{\kern\minuswidth} \catcode`!=\active \def!{\kern\starr}} \begin{document} \noindent{\heada Exam 1} \noindent {\bf STAT401} \hspace{.3in} {\em February 26, 2007} \hspace{1in}Name: \underline{\hspace{3in}} \bigskip \begin{enumerate} \item \textbf{Fill in the Blanks.} (14 pts) Fill in the correct symbol in the space provided. \begin{enumerate} \item An estimator of the population mean is \rule{1in}{.01in}. \medskip \item The sample standard deviation is \rule{1in}{.01in}, and it estimates \rule{1in}{.01in}. \medskip \item The sample correlation is \rule{1in}{.01in} and it estimates \rule{1in}{.01in}. \medskip \item The population proportion is \rule{1in}{.01in}, and it is estimated by \rule{1in}{.01in}. \medskip \end{enumerate} \noindent For the following multiple choice questions, choose the \underline{one} best answer. They are worth 4 points each. \item In order to study insomnia among 1115 patients in a psychiatric hospital, a psychiatrist divides these patients into six disjoint groups by disorder: anxiety (e.g. post traumatic stress syndrome), mood (e.g. depression), psychotic (e.g. schizophrenia), eating (e.g. anorexia), impulse \& addiction, and personality. The psychiatrist then randomly chooses two patients from each group. This is an example of a \underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~}. \begin{enumerate} \item stratified random sample \item cluster sample \item simple random sample \item completely randomized design \item randomized block design \end{enumerate} \item To determine whether GE employees support a new health-care plan, administrators require that any chosen employee must take part in a poll. A pollster randomly selects thirty employees from the company, and then asks ``You don't support the new health-care plan, do you?" The resulting data might suffer from \begin{enumerate} \item Selection bias \item Response bias \item Non-response bias \item There is no bias, a random sample was selected. \end{enumerate} \newpage \newpage The remaining questions require short answers. For those which require computations, SHOW YOUR WORK! \item In June 2006, researchers at Wake Forest University in North Carolina concluded that long term diets containing trans-fats led to alarming patterns of weight gain and insulin resistance in monkeys ({\em Discover}, December 2006). Two groups of vervet monkeys were randomly assigned to one of two different diets: a common ``western style" trans-fat diet or a ``mono-saturated fat" diet (like the fats present in olive oil). \begin{enumerate} \item (4 pts) Give the name of the experimental design used by the Wake Forest researchers. \vspace{.5in} \item (4 pts) List the explanatory variable(s). \vspace{.5in} \item (4 pts) List the response variable(s). \vspace{.5in} \item (4 pts) Explain how a placebo can be used in this study. \vspace{1in} \item (4 pts) Give an extraneous variable which can be directly controlled in this experiment. How can one directly control for this variable? \vspace{1in} \item Over six years, suppose that the twenty-two monkeys in the trans-fat group had the following weight gains (in percentages) \verbatiminput{exam1monkey.txt} \begin{enumerate} \item (6 pts) Determine the five number summary for these measurements. \vspace{1.5 in} \newpage \item (4 pts) Determine the interquartile range. \vspace{.5 in} \item (4 pts) Use the appropriate rule to identify outliers. \vspace{1.5 in} \item (6 pts) Construct a boxplot for this data set. \vspace{1.5in} \end{enumerate} \item (4 pts) Give the sample space for the variable {\bf percent weight gain}. \vspace{.5in} \item (8 pts) Suppose that for monkeys on the six year mono-saturated fat diet, percent weight gain is modeled well by $$X ~\sim ~ N(1.8, .9)$$ \begin{enumerate} \item What proportion of vervet monkeys will actually gain weight after six years on the mono-saturated diet? \vspace{1.5 in} \item What's the probability that two randomly chosen vervet monkeys, after six years on the mono-saturated diet, will both gain weight? \end{enumerate} \end{enumerate} \newpage \item \begin{enumerate} \item (4 pts) Sketch a scatterplot which clearly illustrates a weak negative linear relationship. \vspace{1in} \item (2 pts) Give a plausible sample correlation for this scatterplot. \vspace{.5in} \end{enumerate} \item \begin{enumerate} \item (4 pts) Sketch a scatterplot which clearly illustrates a strong positive non-linear relationship. \vspace{1in} \item (2 pts) Give a plausible sample correlation for this scatterplot. \vspace{.5in} \end{enumerate} \item (12 pts) Let $X$ be the number of milliseconds that it takes for the nervous system of the {\em gryllus bimaculatus} cricket to initially respond to air vibrations from an attacking predator (like a bird or a wasp). The distribution of $X$ is given by \begin{center} \begin{tabular}{|c||c|c|c|c|c|} \hline % after \\: \hline or \cline{col1-col2} \cline{col3-col4} ... $X$ & 3 & 4 & 5 & 6 & 7 or more \\\hline $P(X)$ & 0.14 & 0.27 & 0.28 & 0.18 & 0.13 \\ \hline \end{tabular} \end{center} \begin{enumerate} \item What's the probability that it takes 5 ms or longer for a response? \vspace{1 in} \item For three randomly chosen crickets, what's the probability that all of the crickets' nervous systems respond in 3 ms? \vspace{1.25 in} \item For ten randomly chosen crickets, what's the probability that at least one responds in 3 ms? \vspace{1in} \end{enumerate} \end{enumerate} \end{document} \newpage \item On February 19, 2007, {\em National Public Radio} aired an interview with a ``social scientist" who claimed that people who are more grateful tend to be more happy. Suppose that you wish to design an experiment to test this claim on MSU freshmen. \begin{enumerate} \item Describe how you would sample from the MSU freshmen population using a cluster sample. \vspace{1.5in} \item Describe what the response variable is and how you will measure it. \vspace{1.5in} \item \label{block} Suppose that a proper cluster sample has been performed. Indicate an extraneous variable that you can block in this experiment. \vspace{.5in} \item Give a detailed explanation describing how you will perform the experiment using the blocks from \#\ref{block} and a placebo. \vspace{2in} \item Give one extraneous variable which you will directly control for. How do you directly control this variable? \vspace{1 in} \end{enumerate}