\begin{question}
In a small city the satisfaction with the local public
transportation is evaluated. One question of interest is whether
inhabitants of the city centre are more satisfied with public
transportation compared to those living in the suburbs.
A survey with 250 respondents gave the following contingency table:
\begin{Schunk}
\begin{Soutput}
Location
Evaluation city centre suburbs
very good 24 13
good 38 31
bad 30 61
very bad 8 45
\end{Soutput}
\end{Schunk}
The following table of percentages was constructed:
\begin{Schunk}
\begin{Soutput}
Location
Evaluation city centre suburbs
very good 64.9 35.1
good 55.1 44.9
bad 33.0 67.0
very bad 15.1 84.9
\end{Soutput}
\end{Schunk}
Which of the following statements are correct?
\begin{answerlist}
\item The percentage table can be easily constructed from the original contingency table: percentages are calculated for each column.
\item The percentage table contains row percentages.
\item The value in row~2 and column~2 in the percentage table indicates: 44.9 percentage of those, who evaluated the public transportation as good live in the suburbs.
\item The percentage table gives the satisfaction distribution for each location type.
\item The value in row~1 and column~2 in the percentage table indicates: 35.1 percent of those living in the suburbs evaluated the public transportation as very good.
\end{answerlist}
\end{question}
\begin{solution}
In the percentage table, the row sums are about 100
(except for possible rounding errors). Hence, the table provides
row percentages, i.e.,
conditional proportions for location given satisfaction level.
\begin{answerlist}
\item False. This evaluation gives column percentages. But the table gives row percentages.
\item True. The row sums are about equal to 100 (except for possible rounding errors).
\item True. This is the correct interpretation of row percentages.
\item False. The column sums do not give 100.
\item False. This is an interpretation of column percentages, but the table gives row percentages.
\end{answerlist}
\end{solution}
%% META-INFORMATION
%% \extype{mchoice}
%% \exsolution{01100}
%% \exname{Relative frequencies}