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\begin{center}

\Large{Ryerson  University}

\large{F16 QMS 202 }

\large{ Practice Questions for Lecture 6}

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

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\vspace{0.25cm}

\noindent {\bf Use the following scenario for problems} \ref{q1}-\ref{q4}

\vspace{0.25cm}

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. You would like to know whether the business school preparation course is effective in improving exam scores?

\vspace{1cm}

\begin{center}
\begin{tabular}{|c|c|c|}
\hline
Student & Exam Score Before The Course & Exam Score After The Course \\
\hline 
   1 & 530 & 670  \\
   2 &  690 & 770\\
   3 &  910 & 1000\\
   4 &  700 & 710\\
   5 &   450 & 550 \\
   6 &   820 & 870 \\
   7 &   820 & 770\\
   8 &   630 & 610\\
\hline
\end{tabular}
\end{center}

\vspace{1cm}

\begin{enumerate}

%1
\item What statistical test would you use to test this hypothesis? \label{q1}
%Answer: e
\begin{itemize}
    \item [a)] $\chi^2$ test 
    \item [b)] Two-sample t-test, since the samples are independent.
    \item [c)] Pooled t-test, since the standard deviations of the two populations are the same.
    \item [d)] Z test for the difference between two proportions.
    \item [\circled{e)}] Paired t-test for the mean difference, since the samples are dependent.
    \end{itemize}
%2
\item  If $\mu_1$is used for the population mean of the exam scores before the course, $\mu_2$ for the population mean of the exam scores after the course, and $\mu_D= \mu_1-\mu_2$, the alternative hypothesis for the test would be 
%Answer: c
\begin{itemize}
    \item [a)] $\mu_2 \geq \mu_1$
    \item [b)] $\mu_D \geq 0$
    \item [\circled{c)}] $\mu_D < 0$
    \item [d)] $\mu_D > 0$
    \item [e)] $\mu_1\not =\mu_2$
\end{itemize}
%3
\item  What is the critical value for testing whether the business school preparation course is effective in improving exam scores at the $\alpha= 0.04$ level of significance? 
%Answer: c
\begin{itemize}
    \item [a)] 2.891
    \item [b)] 1.956
    \item [\circled{c)}] -2.046
    \item [d)] -1.956
    \item [e)] None of the above
\end{itemize}
%4
\item  At the $\alpha=0.03$ level of significance, the conclusion for this hypothesis test is that \label{q4}
%Answer: b
\begin{itemize}
    \item [a)] there is sufficient evidence that the business school preparation course does improve exam score.
    \item [\circled{b)}] the evidence indicates that the business school preparation course does not improve exam score.
    \item [c)] there is sufficient evidence that the business school preparation course has no impact on exam score.
    \item [d)] no conclusion can be drawn from the information given.
\end{itemize}

\newpage

%5
\item  An experiment was conducted to study the choices made in mutual fund selection. Undergraduate and MBA students were presented with different S$\&$P 500 index funds that were identical except for fees. Suppose 100 undergraduate students and 100 MBA students were selected. Partial results are shown below:
\vspace{1cm}
\begin{center}
\begin{tabular}{|c|cc|}
\hline
FUND & Undergraduate & MBA \\
\hline 
   Highest-cost Fund & 27 & 18  \\
   Not Highest-cost Fund &  73 & 82\\
   \hline
\end{tabular}
\end{center}
\vspace{1cm}
At the $0.01$ level of significance, is there evidence of a difference between undergraduate and MBA students in the proportion who selected the highest-cost fund?
%Answer: a
\begin{itemize}
    \item [\circled{a)}] There is not enough evidence that the proportion of MBA students who selected highest-cost fund is significantly different from that of Undergraduate students.
    \item [b)] The evidence suggests that the proportion of MBA students who selected highest-cost fund is significantly different from that of Undergraduate students.
    \item [c)] None of the above
\end{itemize}

\vfill \hfill \textbf{-The end-}
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\item  
%Answer: 
\begin{itemize}
    \item [a)] 
    \item [b)] 
    \item [c)] 
    \item [d)] 
    \item [e)] 
\end{itemize}