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\hskip 1.5in \textbf{Midterm 3B--Stat 100--Spring 2001} 
\vskip .2in  
You will need a calculator. 
You may use ONE page of notes (writing/xeroxing allowed  
both sides). Each problem is 
worth 20 points. Different parts of a problem have equal weight unless 
otherwise indicated.  
 Put a box around the final answer to a question. 
\vskip .2in 

\renewcommand{\labelenumi}{\alph{enumi}.}


***NOTE: When you are asked for a confidence interval, 
do NOT   take 
the time to evaluate numbers on your calculator. 
Just write  out the appropriate formula, 
with all   appropriate numbers substituted.***

\vspace{.3in} 

1.
A random sample of 350 American families found that 213 families owned a
home computer.
 Establish a 98\% confidence interval for the proportion of American 
families owning a 
home computer. 
 \vspace{.4in}

2. 
The following summary statistics are recorded for  independent samples
from two populations:


\\ 
\begin{longtable}
{|p{110pt}|p{110pt}|p{110pt}|} a & a & a   \kill 
\hline
	 & Population 1 & Population 2 \\ 
\hline Sample Size & 9    & 11 
\hline Mean & 92.7  & 83.4 \\
\hline Standard deviation & 5.52 & 2.67  \\
\hline
\end{longtable}
\\

(a) (14 points) Construct a 98\% confidence interval for $\mu_1-\mu_2$. 

(b) (4 points) State any assumptions needed to justify your procedure.

(c) (2 points) 
Was your confidence interval a conservative confidence interval? 

\vspace{.4in}

3. 
 A study of postoperative pain relief is conducted to determine
if drug A gives  longer duration pain relief than Drug B.
Observed hours of pain relief are recorded for 55
patients given drug A and 58 patients given drug B.  The summary
statistics are

\vspace{.1in}

\\
\begin{longtable}
{|p{110pt}|p{110pt}|p{110pt}|} a & a & a  \kill \hline & A&
B \\
\hline Mean& 4.64&
4.03 \\
\hline Standard Deviation& 1.25&
1.82 \\
\hline
\end{longtable}
\\
Run the appropriate hypothesis test at level of 
significance   $\alpha = .05$ . In your response, 

\begin{enumerate}
\item
Determine the null and alternative hypotheses.
\item
Define the appropriate test statistic. 
\item
Determine the rejection region.
\item
Determine the observed value of the test statistic.
\item
State your conclusion, report the P-value and comment on the 
strength of your conclusion.  
\end{enumerate}


\vspace{.2in}

**************THERE ARE MORE PROBLEMS ON THE BACK SIDE***************
\vspace{.8in} 

\pagebreak 

\hspace{6in} .  
\vspace{.5in}



4.  A criminologist examined a random sample 
of 16 convicts  serving time for armed 
robbery. 
The mean and standard deviation of their 
sentences were  48 
and 8 months, respectively. 

\vspace{.1in}

(a) (15 points) Determine a $ 95\%$  confidence interval for the 
mean sentence for armed robbery. 

(b) (5 points)  State any assumptions made to justify 
your computation. 

\vspace{.5in}


5. Answer each part TRUE or FALSE. 

\vspace{.1in} 

 (a) If a hypothesis test is run at $\alpha = .01$ and the
P-value is $.03$, then the decision must be to retain 
the null hypothesis. 


\vspace{.1in}

 (b) In  a given population, if the standard deviation 
of $\overline X$ is 20 when $n=25$, then the 
standard deviation of $\overline X$ will be 
$10$ when $n=100$. 


\vspace{.1in}

 (c) If a hypothesis test is run  at significance level $\alpha = .05$ 
on many samples from a population for which the null hypothesis 
is true, 
 then for about $95\%$ of those samples 
 the conclusion will be to retain the null hypothesis. 

\vspace{.1in}

 (d)  If  conservative $95\%$ confidence interval for  the 
difference of two population means are constructed from many 
samples, then the true population mean difference should be in 
at least $95\%$ of those intervals.  

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