\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 = 4.1777, df = 108, p-value = 2.996e-05
alternative hypothesis: true difference in means between group Sparag and group Consumo is greater than 0
95 percent confidence interval:
1.241878 Inf
sample estimates:
mean in group Sparag mean in group Consumo
5.419987 3.360063
\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 4.178.
\item True. The test aims at showing that the difference of means is larger than $0$.
\item False. The $p$~value is equal to $3e-05$.
\item True. The test result is significant ($p < 0.05$) and hence the alternative is shown that the difference of means is larger than 0.
\item False. The test aims at showing that the waiting time at Sparag is longer than at Consumo.
\end{answerlist}
\end{solution}
%% META-INFORMATION
%% \extype{mchoice}
%% \exsolution{11010}
%% \exname{2-sample t-test}