\documentclass[11pt, oneside]{article}   	% use "amsart" instead of "article" for AMSLaTeX format
\usepackage[top=1.5in, bottom=1in]{geometry}                		% See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper}                   		% ... or a4paper or a5paper or ... 
%\geometry{landscape}                		% Activate for rotated page geometry
%\usepackage[parfill]{parskip}    		% Activate to begin paragraphs with an empty line rather than an indent
\usepackage{graphicx}				% Use pdf, png, jpg, or eps§ with pdflatex; use eps in DVI mode
								% TeX will automatically convert eps --> pdf in pdflatex		
\usepackage{amssymb, amsmath}
\usepackage{hyperref}

%SetFonts

%SetFonts


\title{Just the Basics \\
\large for Stat 185
}
\author{}
\date{}

\begin{document}
\maketitle
\pagestyle{empty}
\thispagestyle{empty}



\noindent On our final exam, there will be a ``basics'' section consisting of three problems. Those three problems will be very much like the
problems below but with different numbers. If you can do those three problems - nearly perfectly, then you will pass this class.

\begin{enumerate}
	\item Suppose we randomly select 400 college students and measure their heights in feet. We find that our data has 
	an average of $5.9$ with a standard deviation of $0.42$. We wish to write down a 98\% confidence interval for this data.
        \begin{enumerate}
 		\item Find the standard error associated with this sample.
		\item Use a normal table to find the $z^*$ value that corresponds to a 98\% confidence interval.
		\item Write down a 98\% confidence interval for the average height of college students based on this data.
        \end{enumerate}
        
	\item Suppose we randomly select 4 college students, measure their heights in feet and find them to be
	   \begin{center}\begin{tabular}{c|c|c|c}
          \hline
          5.9 & 5.5 & 6.0 & 6.1
        \end{tabular}\end{center}
        \begin{enumerate}
        	\item Write down a formula showing that the mean of these heights is $5.875$.
		\item Write down a formula showing that the standard deviation of these heights is approximately $0.263$
		\item Find the standard error associated with this sample.
		\item Write down a 95\% confidence interval for the average height of college students based on this data.
        \end{enumerate}

	\item Supposedly, approximately 10\% of the population is left handed, but we think it might be higher than that. 
	Suppose that in a random sample of 75 people, we find 12 left handers. Let's use this data to explore the question 
	of whether the 10\% estimate is truly correct vs whether there might be more than 10\%.
	\begin{enumerate}
		\item Write down the Null and Alternative Hypotheses for this problem.
		\item Compute the standard error, test statistic, and $p$-value.
		\item State the conclusion of the hypothesis test and your reasons why.
	\end{enumerate}
\end{enumerate}


\end{document}  
