Let's solve the problem step-by-step, filling in the two-way table as we go.
Step 1: Determine the total number of vaccinated people.
- Total people: 2,321
- Not vaccinated: 1,085
- Therefore, the total number of vaccinated people is:
[tex]\[
\text{Total vaccinated} = \text{Total people} - \text{Not vaccinated} = 2,321 - 1,085 = 1,236
\][/tex]
Step 2: Calculate the number of vaccinated people who tested negative.
- Vaccinated people who tested positive: 465
- Therefore, the number of vaccinated people who tested negative is:
[tex]\[
\text{Vaccinated negative} = \text{Total vaccinated} - \text{Vaccinated positive} = 1,236 - 465 = 771
\][/tex]
Step 3: Calculate the number of not-vaccinated people who tested positive.
- We know that the total number of people who tested negative is 1,371, so the total number of people who tested positive is:
[tex]\[
\text{Total positive} = \text{Total people} - \text{Total negative} = 2,321 - 1,371 = 950
\][/tex]
- To find the number of not-vaccinated people who tested positive:
[tex]\[
\text{Not vaccinated positive} = \text{Total positive} - \text{Vaccinated positive} = 950 - 465 = 485
\][/tex]
Step 4: Calculate the number of not-vaccinated people who tested negative.
- Total negative people: 1,371
- Vaccinated negative: 771
- Therefore, the number of not-vaccinated people who tested negative is:
[tex]\[
\text{Not vaccinated negative} = \text{Total negative} - \text{Vaccinated negative} = 1,371 - 771 = 600
\][/tex]
Step 5: Complete the two-way table with these values:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Positive} & \text{Negative} & \text{Total} \\
\hline \text{Vaccinated} & 465 & 771 & 1,236 \\
\hline \text{Not Vaccinated} & 485 & 600 & 1,085 \\
\hline \text{Total} & 950 & 1,371 & 2,321 \\
\hline
\end{tabular}
\][/tex]
Thus, the completed two-way table is:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Positive} & \text{Negative} & \text{Total} \\
\hline \text{Vaccinated} & 465 & 771 & 1,236 \\
\hline \text{Not Vaccinated} & 485 & 600 & 1,085 \\
\hline \text{Total} & 950 & 1,371 & 2,321 \\
\hline
\end{tabular}
\][/tex]
