\begin{question}
The waiting time (in minutes) at the cashier of two supermarket
chains with different cashier systems is compared. The following
statistical test was performed:
\begin{Schunk}
\begin{Soutput}
Two Sample t-test
data: Waiting by Supermarket
t = 3.8575, df = 132, p-value = 0.9999
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
-Inf 3.552905
sample estimates:
mean in group Sparag mean in group Consumo
5.859404 3.373846
\end{Soutput}
\end{Schunk}
Which of the following statements are correct? (Significance level $5\%$)
\begin{answerlist}
\item The absolute value of the test statistic is larger than 1.96.
\item A one-sided alternative was tested.
\item The $p$~value is larger than $0.05$.
\item The test shows that the waiting time is longer at Sparag than at Consumo.
\item The test shows that the waiting time is shorter at Sparag than at Consumo.
\end{answerlist}
\end{question}
\begin{solution}
\begin{answerlist}
\item True. The absolute value of the test statistic is equal to 3.857.
\item True. The test aims at showing that the difference of means is smaller than $0$.
\item True. The $p$~value is equal to $1$.
\item False. The test aims at showing that the alternative that the waiting time is shorter at Sparag than at Consumo. The test result is not significant ($p \ge 0.05$).
\item False. The test result ist not significant ($p \ge 0.05$).
\end{answerlist}
\end{solution}
%% META-INFORMATION
%% \extype{mchoice}
%% \exsolution{11100}
%% \exname{2-sample t-test}