\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 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 Suburbs
Very good 19 11
Good 45 31
Bad 25 66
Very bad 11 42
\end{Soutput}
\end{Schunk}
The following table of percentages was constructed:
\begin{Schunk}
\begin{Soutput}
Location
Evaluation City Suburbs
Very good 19.0 7.3
Good 45.0 20.7
Bad 25.0 44.0
Very bad 11.0 28.0
\end{Soutput}
\end{Schunk}
Which of the following statements are correct?
\begin{answerlist}
\item The value in row~3 and column~2 in the percentage table indicates: 44 percent of the respondents in the suburbs evaluated the public transportation as bad.
\item The percentage table provides row percentages.
\item The percentage table can be easily constructed from the original contingency table: Each value is in relation to the total sample size.
\item The value in row 4 and column~2 in the percentage table indicates: 28 percent of those, who evaluated the public transportation as very bad, live in the suburbs.
\item The percentage table provides the satisfaction distribution for each location type.
\end{answerlist}
\end{question}
\begin{solution}
In the percentage table, the column sums are about 100 (except for possible rounding errors).
Hence, the table provides column percentages, i.e., conditional relative frequencies for satisfaction level given location type.
\begin{answerlist}
\item True. This is the correct interpretation for column percentages.
\item False. The row sums are not equal to 100.
\item False. This calculation yields total percentages. But the table provides column percentages.
\item False. This is an interpretation for row percentages, but the table provides column percentages.
\item True. The column sums are equal to 100 (except for possible rounding errors).
\end{answerlist}
\end{solution}
%% META-INFORMATION
%% \extype{mchoice}
%% \exsolution{10001}
%% \exname{Relative frequencies}