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\begin{center}

\Large{Ryerson  University}

\large{F16 QMS 202 }

\large{ Practice Questions for Lecture 4}

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

\end {center}

\begin{enumerate}

\vspace{1cm}

%1
\item A sample of size $n=160$ is selected from the left-skewed population with $\overline{X}=100$ and $S=21$. Which of the following statements is true?
%Answer:  a
\begin{itemize}
    \item [\circled{a)}] We can use the t-test to test the null hypothesis $H_0 : \mu = 105$
    \item [b)]    We can use the Z-test to test the null hypothesis $H_0 : \mu = 105$ 
    \item [c)] We cannot use the t-test to test the null hypothesis $H_0 : \mu = 105$ because the population is not normally distributed
    \item [d)] We cannot use the t-test to test the alternative hypothesis $H_0 : \mu = 105$ because the sample is too small.
    \end{itemize}

\noindent {\bf Use the following scenario for problems} \ref{q2}-\ref{q5}

A company that manufactures chocolate bars is particularly concerned about the mean weight of chocolate bars. A sample of 18 chocolate bars is selected, and their weights in ounces are summarized in the following table 
\begin{center}
\begin{tabular}{|c c c c c c|}
\hline
6.029  &  6.089  &  6.056  &  6.051  &  6.110  &  6.068  \\
6.098  &  6.096  &  6.011  &  6.009  &  6.033  &  6.000 \\
5.995  &  5.990  &  6.110  &  5.990  &  5.955  &  5.922 \\
\hline
 \end{tabular}    
 \end{center}  
Assume normal distribution of weights of chocolate bars. 

%2
\item The parameter of interest for this study is? \label{q2}
%Answer:  d
\begin{itemize}
    \item [a)] $\sigma $
    \item [b)] $\pi $
    \item [c)] $\overline{X}$
    \item [\circled{d)}]  $\mu$
\end{itemize}
%3
\item  The null and alternative hypotheses to determine if the mean weight of the chocolate bars is greater that $6.02$ ounces are?
%Answer:  a
\begin{itemize}
    \item [\circled{a)}] $ H_0: \mu \leq 6.02 \quad \mbox{and}\quad  H_1: \mu > 6.02$
    \item [b)] $H_0: \mu \geq 6.02 \quad \mbox{and}\quad  H_1: \mu < 6.02 $
    \item [c)] $ H_0: \overline{X} \quad \geq 6.02\quad \mbox{and} \quad H_1: \overline{X} < 6.02$
    \item [d)] $H_0: \overline{X}=6.02 \quad \mbox{and} \quad H_1: \overline{X}\not = 6.02 $
\end{itemize}
%4
\item  The correct rejection region for $H_0$ at $\alpha = 0.05$ is 
%Answer:  b
\begin{itemize}
    \item [a)] Reject $H_0$ if   $t_{\tiny STAT} < -1.74$
    \item [\circled{b)}] Reject $H_0$ if   $t_{\tiny STAT} > 1.74$
    \item [c)] Reject $H_0$ if   $t_{\tiny STAT} > 1.98$ or $Z_{\tiny STAT} < -1.98$
    \item [d)]  None of the above
\end{itemize}
 %5
 \item Which of the following conclusions is correct? \label{q5}
%Answer:  b
\begin{itemize}
    \item [a)] At $\alpha = 0.15$, there is sufficient evidence to conclude that the population mean weight of the chocolate bars is 6.02 ounces.
    \item [\circled{b)}] At $\alpha = 0.15$, there is sufficient evidence to conclude that the population mean weight of the chocolate bars is greater than 6.02 ounces.
    \item [c)] At $\alpha = 0.10$, there is sufficient evidence to conclude that the population mean weight of the chocolate bars is greater than 6.02 ounces.
    \item [d)] At $\alpha = 0.05$, there is sufficient evidence to conclude that the population mean weight of the chocolate bars is greater than 6.02 ounces.
\end{itemize}

\noindent {\bf Use the following scenario for problems} \ref{q6}-\ref{q9}

A company that manufactures coffee vending machines has developed a new process ensuring that coffee cups are filled correctly. The previous process filled the cups  correctly $85\%$ of the time. Based on a sample of 100 orders, using the new process, 94 were filled correctly. The company would like to know whether the new process has increased the proportion of orders filled correctly.

%6
\item What null hypothesis would you choose for this study? \label{q6}
%Answer:  d
\begin{itemize}
    \item [a)]  $H_0: \pi \geq 85$
    \item [b)] $H_0: \pi \leq 85$
    \item [c)]  $H_0: \pi \geq 0.85$
    \item [\circled{d)}] $H_0: \pi \leq 0.85$
\end{itemize}
%7
\item At the $0.01$ level of significance, what critical value should the company officials use to determine the rejection region?
%Answer: c
\begin{itemize}
    \item [a)] 1.96    
    \item [b)] 1.66
    \item [\circled{c)}]  2.33    
    \item [d)] 2.07
\end{itemize}
%8
\item Which of the following statements is false?
%Answer:  d
\begin{itemize}
    \item [a)]   the null hypothesis would not be rejected if a $0.1\%$ probability of committing a Type I error is allowed.
    \item [b)]   the null hypothesis would be rejected if a $2.5\%$ probability of committing a Type I error is allowed.
    \item [c)]   the null hypothesis would be rejected if a $5\%$ probability of committing a Type I error is allowed.
    \item [\circled{d)}] the null hypothesis would not be rejected if a $10\%$ probability of committing a Type I error is allowed.
\end{itemize}
%9
\item What will be the p-value if these data were used to perform a two-tail test? \label{q9}
%Answer:  a
\begin{itemize}
    \item [\circled{a)}] 0.0117
    \item [b)] 0.0225
    \item [c)] 0.0725
    \item [d)] 0.1725
\end{itemize}
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