To determine which statement is true based on the survey results, let's analyze the data step-by-step.
1. Visualize the Data:
We have a table with preferences of students and teachers for the new school mascot:
[tex]\[
\begin{array}{|l|c|c|c|}
\hline & \text{Pirates} & \text{Moose} & \text{Total} \\
\hline \text{Students} & 75 & 15 & 90 \\
\hline \text{Teachers} & 5 & 15 & 20 \\
\hline \text{Total} & 80 & 30 & 110 \\
\hline
\end{array}
\][/tex]
2. Statement Analysis:
Let's evaluate each statement:
- Statement A: There is no difference between the preferences of students and teachers.
- This statement would be true if students and teachers had the same number of votes for each option. By comparing the numbers, we see that the votes are different (75 students vs. 5 teachers for Pirates, and 15 students vs. 15 teachers for Moose).
- Statement B: "Moose" is equally popular with students and teachers.
- Both students and teachers have given 15 votes for Moose, so this statement is true.
- Statement C: "Moose" is more popular with students, but "Pirates" is more popular with teachers.
- From the table, 15 students and 15 teachers favor Moose (equally popular), thus this statement is false. Also, Pirates are favored by 75 students compared to 5 teachers.
- Statement D: "Pirate" is more popular with students, but "Moose" is more popular with teachers.
- From the table, 75 students prefer Pirates compared to 5 teachers (Pirates are more popular among students). While the Moose preference is the same between students and teachers (15 each), "more popular" is not correct.
Hence, the only statement that aligns with the provided data is:
B. "Moose" is equally popular with students and teachers.
However, given that the result from prior analysis is [tex]\(4\)[/tex] (which corresponds to statement D), there could be a misunderstanding. Let's verify:
Almost certainly, a mistake was made. Here we should select statement B, as no preference differentiation between students and teachers.
