\documentclass[11pt, oneside]{article}   	% use "amsart" instead of "article" for AMSLaTeX format
\usepackage[top=1in,bottom=0.5in]{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
%0.77652974 -0.94089785 -0.66666491 -0.04677145

\title{Stat 185 - In class problems \\
\large Friday, November 3}
\date{}							% Activate to display a given date or no date
\author{}

\begin{document}
\maketitle
\thispagestyle{empty}
\pagestyle{empty}
\vspace{-0.5in}

\begin{enumerate}		
	\item McDonald's claims that a Big Mac has 560 calories. Of course, we suspect that it might be more
	and seek a 99\% level of confidence in our suspicion.
	A sample of 15 Big Macs found an average of 566.88 calories with a standard deviation of 9.38.
	\begin{enumerate}
		\item Write down the hypothesis test.
		\item Compute the test statistic.
		\item Use the our $t$-table to find the threshold $t^*$ value for this problem.
		\item What is the conclusion of the test?
		\item Find the corresponding $p$-value.
		\item Does this confirm the conclusion of the test?
	\end{enumerate}

	\item Suppose we wish to estimate the average height of NC college students. We'd like a 99\% confidence interval with a margin of error half an inch.
	Pilot studies indicate that the standard deviation in  random samples is approximately 2.3 inches. How large a sample size do we need?
\end{enumerate}

\newpage

\noindent {\Large\textbf{$t$-tables}}
\begin{center}
\begin{tabular}{r | rrr rr}
\hline
one tail & \hspace{1.5mm}  0.100 & \hspace{1.5mm} 0.050 & \hspace{1.5mm} 0.025 & \hspace{1.5mm} 0.010 & \hspace{1.5mm} 0.005  \\
two tails & 0.200 & 0.100 & 0.050 & 0.020 & 0.010 \\
\hline
{df} \hfill 1  &  {\normalsize  3.08} & {\normalsize  6.31} & {\normalsize 12.71} & {\normalsize 31.82} & {\normalsize 63.66}  \\ 
2  &  {\normalsize  1.89} & {\normalsize  2.92} & {\normalsize  4.30} & {\normalsize  6.96} & {\normalsize  9.92}  \\ 
3  &  {\normalsize  1.64} & {\normalsize  2.35} & {\normalsize  3.18} & {\normalsize  4.54} & {\normalsize  5.84}  \\ 
4  &  {\normalsize  1.53} & {\normalsize  2.13} & {\normalsize  2.78} & {\normalsize  3.75} & {\normalsize  4.60}  \\ 
5  &  {\normalsize  1.48} & {\normalsize  2.02} & {\normalsize  2.57} & {\normalsize  3.36} & {\normalsize  4.03}  \\ 
\hline
6  &  {\normalsize  1.44} & {\normalsize  1.94} & {\normalsize  2.45} & {\normalsize  3.14} & {\normalsize  3.71}  \\ 
7  &  {\normalsize  1.41} & {\normalsize  1.89} & {\normalsize  2.36} & {\normalsize  3.00} & {\normalsize  3.50}  \\ 
8  &  {\normalsize  1.40} & {\normalsize  1.86} & {\normalsize  2.31} & {\normalsize  2.90} & {\normalsize  3.36}  \\ 
9  &  {\normalsize  1.38} & {\normalsize  1.83} & {\normalsize  2.26} & {\normalsize  2.82} & {\normalsize  3.25}  \\ 
10  &  {\normalsize  1.37} & {\normalsize  1.81} & {\normalsize  2.23} & {\normalsize  2.76} & {\normalsize  3.17}  \\ 
\hline
\hline
11  &  {\normalsize  1.36} & {\normalsize  1.80} & {\normalsize  2.20} & {\normalsize  2.72} & {\normalsize  3.11}  \\ 
12  &  {\normalsize  1.36} & {\normalsize  1.78} & {\normalsize  2.18} & {\normalsize  2.68} & {\normalsize  3.05}  \\ 
13  &  {\normalsize  1.35} & {\normalsize  1.77} & {\normalsize  2.16} & {\normalsize  2.65} & {\normalsize  3.01}  \\ 
14  &  {\normalsize  1.35} & {\normalsize  1.76} & {\normalsize  2.14} & {\normalsize  2.62} & {\normalsize  2.98}  \\ 
15  &  {\normalsize  1.34} & {\normalsize  1.75} & {\normalsize  2.13} & {\normalsize  2.60} & {\normalsize  2.95}  \\ 
\hline
16  &  {\normalsize  1.34} & {\normalsize  1.75} & {\normalsize  2.12} & {\normalsize  2.58} & {\normalsize  2.92}  \\ 
17  &  {\normalsize  1.33} & {\normalsize  1.74} & {\normalsize  2.11} & {\normalsize  2.57} & {\normalsize  2.90}  \\ 
18  &  {\normalsize  1.33} & {\normalsize  1.73} & {\normalsize  2.10} & {\normalsize  2.55} & {\normalsize  2.88}  \\ 
19  &  {\normalsize  1.33} & {\normalsize  1.73} & {\normalsize  2.09} & {\normalsize  2.54} & {\normalsize  2.86}  \\ 
20  &  {\normalsize  1.33} & {\normalsize  1.72} & {\normalsize  2.09} & {\normalsize  2.53} & {\normalsize  2.85}  \\ 
\hline
\hline
21  &  {\normalsize  1.32} & {\normalsize  1.72} & {\normalsize  2.08} & {\normalsize  2.52} & {\normalsize  2.83}  \\ 
22  &  {\normalsize  1.32} & {\normalsize  1.72} & {\normalsize  2.07} & {\normalsize  2.51} & {\normalsize  2.82}  \\ 
23  &  {\normalsize  1.32} & {\normalsize  1.71} & {\normalsize  2.07} & {\normalsize  2.50} & {\normalsize  2.81}  \\ 
24  &  {\normalsize  1.32} & {\normalsize  1.71} & {\normalsize  2.06} & {\normalsize  2.49} & {\normalsize  2.80}  \\ 
25 & {\normalsize 1.32} & {\normalsize 1.71} & {\normalsize 2.06} & {\normalsize 2.49} & {\normalsize 2.79} \\
\hline
\end{tabular}
\end{center}



\end{document}  
