To determine which data table indicates a positive linear association between the hours worked and the daily wages of waiters in a restaurant, we need to check whether the daily wages increase as the hours worked increase.
Let's examine each table in detail:
Table A:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Hours Worked} & \text{Daily Wage (\$)} \\
\hline
9 & 45 \\
8 & 40 \\
7 & 45 \\
6 & 40 \\
\hline
\end{array}
\][/tex]
In Table A, the daily wages do not consistently increase as the hours worked increase. For instance, at 8 hours the wage is 40, but at 7 hours the wage jumps to 45. Hence, there is no positive linear association here.
Table B:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Hours Worked} & \text{Daily Wage (\$)} \\
\hline
9 & 45 \\
8 & 45 \\
7 & 45 \\
6 & 45 \\
\hline
\end{array}
\][/tex]
In Table B, the daily wage is constant at 45 regardless of the hours worked. Since there is no change in wages with changes in hours worked, there is no positive linear association.
Table C:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Hours Worked} & \text{Daily Wage (\$)} \\
\hline
6 & 30 \\
7 & 35 \\
8 & 40 \\
9 & 45 \\
\hline
\end{array}
\][/tex]
In Table C, the daily wage increases as the hours worked increase. As you move from 6 to 9 hours, the daily wage increases steadily from 30 to 45. This indicates a positive linear association between hours worked and daily wages.
Conclusion:
From the analysis above, it is clear that the table indicating a positive linear association between the hours worked and the daily wages is:
D. Table C
