Let's complete the table and the sentence beneath it step-by-step.
First, fill in the rest of the table by combining each girl with each boy:
\begin{tabular}{|c|c|c|c|c|}
\hline & & \multicolumn{3}{|c|}{ Boys } \\
\hline & & Neil & Barney & Ted \\
\hline \multirow{3}{}{ Girls } & Michaela & N-M & B-M & T-M \\
\hline & Candice & N-C & B-C & T-C \\
\hline & Raven & N-R & B-R & T-R \\
\hline
\end{tabular}
Now, count the number of possible combinations (sample size). Each girl can be combined with each boy, so the total number of combinations is:
- Michaela with Neil, Barney, Ted
- Candice with Neil, Barney, Ted
- Raven with Neil, Barney, Ted
That’s 3 girls times 3 boys, which gives a total of 9 combinations. Therefore, the initial sample size is 9.
Now, if the number of choices for girls and boys both increased to 4, we would calculate the new sample size similarly. Each of the 4 girls would be combined with each of the 4 boys:
- The new sample size = 4 girls 4 boys = 16 combinations.
The final answer for the sentence beneath the table:
"If instead of three girls and three boys, there were four girls and four boys to choose from, the new sample size would be 16."
