\setcounter{ExampleCounter}{1}
\paragraph{Observational Study:} the investigators don't actively affect the subjects of the study; they simply observe what they do and what happens to them (ex: tobacco studies)
\paragraph{Experimental Study:} the investigators assign subjects to different groups and vary the conditions for each group, observing the results (ex: pharmaceutical studies)
\subsection{Experimental Study Terms}
\begin{itemize}
\item \textbf{Experimental unit:} the individuals being studied (people, animals, objects, etc.)
\item \textbf{Response:} what we measure about these individuals (ex: blood pressure based on new medication)
\item \textbf{Explanatory variable:} a variable that causes a change in the response; the goal is to identify an explanatory variable and see how much of a change it causes (ex: dosage of new medication)
\item \textbf{Treatment:} the different values of the explanatory variable that we give to the experimental units; we divide them into treatment groups
\item \textbf{Lurking variable:} an additional variable that can obscure the results of a study (ex: men tend to have higher blood pressure than women)
\item \textbf{Control group:} a treatment group to which nothing is done (except a placebo)
\item \textbf{Placebo:} a fake treatment
\item \textbf{Blinding:} ensuring that those involved in the study don't know what treatment group they belong to (hence the use of placebos); double-blind: even the researchers don't know
\end{itemize}
\vfill
\pagebreak
\begin{example}{Experimental Design}
Researchers want to investigate whether taking aspirin regularly reduces the risk of heart attack. Four hundred men between the ages of 50 and 84 are recruited as participants. The men are divided randomly into two groups: one group will take aspirin, and the other group will take a placebo. Each man takes one pill each day for three years. At the end of the study, researchers count the number of men in each group who have had heart attacks.\\
Identify each of the following in this study:\\
\begin{itemize}
\item \textbf{Population:} All men aged 50 to 84
\item \textbf{Sample:} The 400 men selected for the study
\item \textbf{Experimental units:} The individual men in the study
\item \textbf{Control group:} The group taking the placebo
\item \textbf{Explanatory variable:} The medication
\item \textbf{Treatments:} Aspirin or placebo
\item \textbf{Response variable:} Whether or not a subject had a heart attack
\end{itemize}
\end{example}
\blankpage
\begin{exercises}
\textit{For problems 1--2, identify each of the given components of the study.}\\
\ptwo{A fitness center is interested in the mean amount of time a client spends exercises in the center each week.
\begin{enumerate}[(a)]
\item Population: \textbf{all clients}
\vspace{0.2in}
\item Sample: \textbf{the clients they survey}
\vspace{0.2in}
\item Parameter: \textbf{average time spent for all clients}
\vspace{0.2in}
\item Statistic: \textbf{average time spent for surveyed clients}
\vspace{0.2in}
\item Variable: \textbf{time spent for a particular client}
\vspace{0.2in}
\end{enumerate}}
\ptwo{A marriage counselor is interested in the proportion of clients she counsels who stay married.
\begin{enumerate}[(a)]
\item Population: \textbf{all her clients}
\vspace{0.2in}
\item Sample: \textbf{the clients she surveys}
\vspace{0.2in}
\item Parameter: \textbf{proportion of her clients who stay married}
\vspace{0.2in}
\item Statistic: \textbf{proportion of the surveyed clients who stay married}
\vspace{0.2in}
\item Variable: \textbf{whether or not a particular couple stays married}
\vspace{0.2in}
\end{enumerate}}
\textit{For problems 3--8, determine the type of sampling used.}\\
\ptwo{A high school principal polls 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors regarding policy changes for after school activities.\\
Sampling Method: \textbf{Stratified}\\}
\ptwo{To check their accuracy, the Census Bureau draws a sample of several city blocks and recounts everyone in those blocks.\\
Sampling Method: \textbf{Cluster}\\}
\ptwo{A pollster walks around a busy shopping mall and asks people passing by how often they shop at the mall.\\
Sampling Method: \textbf{Convenience}\\}
\ptwo{A restaurant samples 100 sales from the past week by numbering all their receipts, generating 100 random numbers, and picking the receipts that correspond to those numbers.\\
Sampling Method: \textbf{Simple Random}\\}
\ptwo{Police at a DUI checkpoint stop every tenth car to check whether the driver is sober.\\
Sampling Method: \textbf{Systematic}\\}
\ptwo{The provost at a university wants to know how a particular policy is affecting faculty, so she randomly selects 3 members of each department to survey.\\
Sampling Method: \textbf{Stratified}\\}
\pagebreak
\textit{For problems 9--10, determine whether an observational study or experimental study is more appropriate. Explain your answer.}\\
\ptwo{A scientist wants to determine whether people who live at higher altitudes are more or less likely to develop respiratory problems than people who live at lower altitudes.\\
\textbf{Observational; can't make people move}
\vspace{0.75in}}
\ptwo{A scientist wants to determine whether a certain nasal spray is effective in reducing allergic reactions to pollen.\\
\textbf{Experimental}}
\pone{A recent study compared the heart rates of 19 infants born to nonsmoking mothers with those of 17 infants born to mothers who smoked an average of 15 cigarettes a day while pregnant and after giving birth. The heart rates of the infants at one year of age were 20\% slower on the average for the smoking mothers.
\begin{enumerate}[(a)]
\item What were the experimental units? \hfill \textbf{Babies}
\vspace{0.75in}
\item What was the response? \hfill \textbf{Heart rate}
\vspace{0.75in}
\item What were the treatments? \hfill \textbf{Smoking and nonsmoking mothers}
\vspace{0.75in}
\item Give one suggestion that you would make to improve this study, as it is stated. \hfill \textbf{Ex: larger sample}
\end{enumerate}}
\end{exercises}