Alright, let's go through the steps required to complete the table and the sentence beneath it.
1. Complete the Table:
- Each cell in the table should show the pairs of girls and boys.
- In each pair, a girl is represented by her initial (M for Michaela, C for Candice, R for Raven), and a boy is also represented by his initial (N for Neil, B for Barney, T for Ted).
Here is the completed table:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
& & \multicolumn{3}{|c|}{\text{Boys}} \\
\hline
& & \text{Neil} & \text{Barney} & \text{Ted} \\
\hline
\multirow{3}{*}{\text{Girls}} & \text{Michaela} & \text{N-M} & \text{B-M} & \text{T-M} \\
\hline
& \text{Candice} & \text{N-C} & \text{B-C} & \text{T-C} \\
\hline
& \text{Raven} & \text{N-R} & \text{B-R} & \text{T-R} \\
\hline
\end{array}
\][/tex]
2. Calculate the Number of Pairings:
- Originally, there are 3 girls and 3 boys.
- The number of different pairs that can be formed from 3 girls and 3 boys is given by multiplying the number of girls by the number of boys: \(3 \times 3 = 9\).
3. New Sample Size:
- If there are now 4 girls and 4 boys, the number of pairs will be:
- Multiply the number of girls by the number of boys: \(4 \times 4 = 16\).
So the new sample size would be [tex]\(16\)[/tex].
