Let's break down the given data and fill out the two-way table step by step:
1. The total number of people in the study is 2,321.
2. Out of these, 1,085 people did not receive a flu vaccination. Therefore, the number of people who were vaccinated is:[tex]\(1236 (2321 - 1085)\)[/tex].
3. 465 people who were vaccinated tested positive for the flu.
4. A total of 1,371 participants tested negative for the flu.
To fill out the table completely, we need to find the following numbers:
- The number of people who were vaccinated and tested negative for the flu.
- The number of people who were not vaccinated and tested positive for the flu.
- The number of people who were not vaccinated and tested negative for the flu.
First, we will figure out how many people were vaccinated and tested negative for the flu:
[tex]\[1236 (Number\ of\ vaccinated\ people) - 465 (Vaccinated\ and\ positive) = 771\ (Vaccinated\ and\ negative)\][/tex]
Next, find the total number of participants who tested positive for the flu:
[tex]\[2321 (Total\ number\ of\ people) - 1371 (Total\ negative) = 950\ (Total\ positive)\][/tex]
Now, let's find the number of people who were not vaccinated and tested positive for the flu:
[tex]\[950 (Total\ positive) - 465 (Vaccinated\ and\ positive) = 485\ (Not\ vaccinated\ and\ positive)\][/tex]
Finally, find the number of people who were not vaccinated and tested negative for the flu:
[tex]\[1085 (Not\ vaccinated) - 485 (Not\ vaccinated\ and\ positive) = 600\ (Not\ vaccinated\ and\ negative)\][/tex]
Now, we can fill in the complete two-way table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & Positive & Negative & Total \\
\hline Vaccinated & 465 & 771 & 1236 \\
\hline Not Vaccinated & 485 & 600 & 1085 \\
\hline Total & 950 & 1371 & 2321 \\
\hline
\end{tabular}
\][/tex]
