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\begin{center}

\Large{Ryerson  University}

\large{F16 QMS 202 }

\large{ Practice Questions for Lecture 1}

\large{ Dr Bo\v za Tasi\' c} 

\end {center}

\begin{enumerate}

%1
\item The Z-values associated with $99\%$ confidence (i.e., probability 0.99) are
%Answer:  D
\begin{itemize}
    \item [a)] -1.96 and 1.96
    \item [b)] -2.55 and 2.55
    \item [c)] -2.57 and 2.57
    \item [d)] -2.58 and 2.58
    \end{itemize}
%2
\item If  $\overline X=125, \, \sigma = 24$, and $n=36$, the $99\%$ confidence interval estimate for the population mean $\mu$ is 
%Answer:  C
\begin{itemize}
    \item [a)] $102.45 \leq \mu \leq 127.88$
    \item [b)] $92.55 \leq \mu \leq 107.86$
    \item [c)] $114.70 \leq \mu \leq 135.30$ 
    \item [d)] $100.45 \leq \mu \leq 117.88$ 
 \end{itemize}
%3
\item Determine the critical value of $ t$  in the following circumstances: \[1- \alpha = 0.90, \, n= 16. \] Round your answer to 4 decimal places!  
%Answer:  1.7531

{\bf Answer:}

%4
 \item It is desired to estimate the mean total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the $95\%$ confidence interval was calculated to be $(\$2,181,260, \$5,836,180)$. Which of the following interpretations is correct?
%Answer:  D
\begin{itemize}
    \item [a)] $95\%$ of the sampled total compensation values fell between $\$ 2,181,260$ and $\$ 5,836,180$.
    \item [b)] We are $95\%$ confident that the mean of the sampled CEOs falls in the interval $\$2,181,260$ to $\$5,836,180$.
    \item [c)] In the population of Service industry CEOs, $95\%$ of them will have total compensations that fall in the interval $\$2,181,260$ to $\$5,836,180$.
    \item [d)] We are $95\%$ confident that the mean total compensation of all CEOs in the Service industry falls in the interval $\$2,181,260$ to $\$ 5,836,180$.
 \end{itemize}
%5
\item An economist is interested in studying the incomes of consumers in a particular country. The population standard deviation is known to be $\$1000$. A random sample of 50 individuals resulted in a mean income of $\$15000$. What is the width of the $90\%$ confidence interval rounded to two decimal places? Remark:  The width (length) of an interval $(a,\,b)$ is $b-a$. 
%Answer:  465.23

{\bf Answer:}

%6
\item The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant to use 25 days of data to construct the interval estimate, what confidence level can she attach to the interval estimate?   
%Answer:  A
\begin{itemize}
    \item [a)] 99.7 $\%$
    \item [b)] 99.0 $\%$
    \item [c)] 98.0 $\%$
    \item [d)] 95.4 $\%$
 \end{itemize}


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