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\begin{flushright}
Name \underline{\hspace{60mm}} \\ 
$\,$ \\
Student Number \underline{\hspace{60mm}}
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\begin{center}   
{\Large \textbf{STA 441s 2024 Quiz 3}}\\
\vspace{3 mm}
\end{center}


\begin{enumerate} 

\item (4 points) In a study comparing the effectiveness of different exercise programmes, volunteers were randomly assigned to one of three exercise programmes ($A$, $B$, $C$) or put on a waiting list and told to work out on their own. Thus, there were four experimental treatments. Denote the true treatment means by 
$\mu_a, \mu_b, \mu_c$ and $\mu_w$.

Aerobic capacity is the body's ability to process oxygen. Using a standard treadmill test, aerobic capacity was measured before and after 6 months of participation in the program (or 6 months of being on the waiting list). The response variable was improvement in aerobic capacity. 

    \begin{enumerate}

        \item What null hypothesis would you test to determine whether experimental treatment (including the control) had any effect on average improvement in aerobic capacity? State the null hypothesis in symbols. \vspace{10mm}
    
        \item For the test of whether experimental treatment had any effect on average improvement in aerobic capacity, give the contrast or contrasts you would test.  Make a table. There is one column in your table for each treatment mean, and one row for each contrast.  \vspace{30mm}
    
        \item What null hypothesis would you test to determine whether the average improvement from the three exercise programs was greater than improvement from the wait list control?  State the null hypothesis in symbols. \vspace{10mm}

        \item For the test of whether average improvement from the three exercise programs was greater than improvement from the wait list control, give the contrast or contrasts you would test.   Make a table.  There is one column in your table for each treatment mean, and one row for each contrast.

    \end{enumerate}

\pagebreak
    
\item \label{computer} Please refer to your analysis of the Chick Weights data.
    \begin{enumerate}

        \item (1 point) \label{rsq} What proportion of the variation in the chicks' weight is explained by type of feed? The answer is a number on your printout. Write the number in the space below. on the printout, circle the number and write ``Question~\ref{rsq}" beside it.  \vspace{10mm}


        \item (5 points) In your analysis of the Chick Weights data, you used Tukey multiple comparisons to test for all pairwise differences between means, at joint significance level 0.05. Based on this, answer each of the questions below ``Yes" or ``No." \emph{To get any marks for this question, you can get no more than one wrong.}  \vspace{5mm}
            \begin{itemize}
                \item   Is there sufficient evidence to conclude that sunflower is better than casin?    \vspace{5mm}
                \item   Is there sufficient evidence to conclude that casin is better than meatmeal?    \vspace{5mm}
                \item   Is there sufficient evidence to conclude that meatmeal is better than soybean?    \vspace{5mm}
                \item   Is there sufficient evidence to conclude that soybean is better than linseed?    \vspace{5mm}
                \item   Is there sufficient evidence to conclude that linseed is better than horsebean?    \vspace{5mm}
                \item   Is there sufficient evidence to conclude that sunflower is better than horsebean?    \vspace{5mm}
                \item   Is there sufficient evidence to conclude that casin is better than soybean?    \vspace{5mm}
            \end{itemize}
        
    \end{enumerate}

\end{enumerate}

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\begin{center}
\textbf{Attach your log file and your results file to the quiz paper. Make sure your name and student number are written clearly on both printouts.}
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