\documentclass[12pt]{article} 
%\usepackage{amsbsy} % for \boldsymbol and \pmb 
%\usepackage{graphicx} % To include pdf files!
\usepackage{amsmath}
\usepackage{amsbsy}
\usepackage{amsfonts}
%\usepackage[colorlinks=true, pdfstartview=FitV, linkcolor=blue, citecolor=blue, urlcolor=blue]{hyperref} % For links
\usepackage{fullpage}           % Good for US Letter paper

\topmargin=-0.75in
\textheight=9.5in
\usepackage{fancyhdr} 
\renewcommand{\headrulewidth}{0pt}  % Otherwise there's a rule under the header
\setlength{\headheight}{15.2pt}
\fancyhf{}
\pagestyle{fancy} 
\cfoot{Page \thepage {} of 2}
%

% \pagestyle{empty} % No page numbers

\begin{document}
%\enlargethispage*{1000 pt} 

\begin{flushright}
Name \underline{\hspace{60mm}} \\ 
$\,$ \\
Student Number \underline{\hspace{60mm}}
\end{flushright}   
\vspace{2mm}

\begin{center}   
{\Large \textbf{STA 312 f2023 Quiz 7}}\\
\vspace{1 mm}
\end{center}   

\begin{enumerate}

\item (4 points) Let the continuous random variable $X$ have density $f_x(x) = \exp\{x-e^x \}$, for all real $x$. Find the density of $Y=e^X$. Show your work. Please be sure to specify where the density of $Y$ is non-zero, and where it is zero.

\pagebreak %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\item (3 points) For the regression equation 
$y_i = \beta_0 + \beta_1x_{i,1} + \beta_2x_{i,2} + \beta_3x_{i,3} + \epsilon_i$,
the response variable $y_i$ is the cumulative grade point average (GPA) of High School student $i$, $x_{i,1}$ is family income, $x_{i,2}$ is mother's education, and $x_{i,3}$ is father's education. Give the null hypothesis you would test to answer the following questions. A null hypothesis is a statement about the model parameters.
    \begin{enumerate}
        \item Once you correct for parents' education, is GPA still related to family income?
        \vspace{10mm}
        \item Allowing for family income, is GPA related to parents' education?
        \vspace{10mm}
        \item Once you control for family income and mother's education, is GPA related to father's education?
        \vspace{10mm}
    \end{enumerate}

 \item \label{comp} In Question 8 of Assignment 7, you analyzed data from a sample of pigs. Consider this question: Adjusting for mother's weight and father's weight, which drug helps the average pig gain more weight, Drug~1 or Drug~2?
                \begin{enumerate}
                    \item (1/2 point) \label{Ft} In the space below, write the $F$ or $t$ statistic, a number from your printout. On your printout, circle the number and write ``Question~\ref{Ft}" beside it.
                            \vspace{10mm}
                    \item (1/2 point) \label{pval} In the space below, write the $p$-value, a number from your printout. On your printout, circle the number and write ``Question~\ref{pval}" beside it.
                    \vspace{10mm}
                    \item (2 points) \label{concl} In plain, non-statistical language, what do you conclude from this test? Your answer should be guided by the $\alpha=0.05$ significance level, but you must not mention that, because this is a plain language answer. You cannot get any marks for this part unless the test statistic and $p$-value are correct.
                    \vspace{50mm}
                \end{enumerate}

 
 


\end{enumerate}

\noindent
Please attach the printout(s) with your answers to Question~8 of the assignment, showing all the input and output. \textbf{Make sure your name and student number are written on the printout}.

\end{document}