A survey asks teachers and students whether they would like the new school mascot to be a shark or a moose. The table below shows the results. Which statement is true?

\begin{tabular}{|l|c|c|c|}
\hline
& Sharks & Moose & Total \\
\hline
Students & 90 & 10 & 100 \\
\hline
Teachers & 5 & 10 & 15 \\
\hline
Total & 95 & 20 & 115 \\
\hline
\end{tabular}

A. "Moose" is equally popular with students and teachers.
B. There is no difference between the preferences of students and teachers.
C. "Shark" is more popular with students, but "moose" is more popular with teachers.
D. "Moose" is more popular with students, but "shark" is more popular with teachers.



Answer :

Let's analyze each of the given statements in relation to the provided survey data to determine which is true:

1. Statement A: "Moose" is equally popular with students and teachers.

To verify this statement, we need to compare the number of students and teachers who prefer "Moose".
- According to the survey, 10 students prefer "Moose".
- Similarly, 10 teachers prefer "Moose".

Since both the number of students and teachers preferring "Moose" is the same (10), this statement is true.

2. Statement B: There is no difference between the preferences of students and teachers.

To verify this statement, we need to examine the overall preferences:
- Students: 90 prefer "Shark", 10 prefer "Moose".
- Teachers: 5 prefer "Shark", 10 prefer "Moose".

There is a clear difference between the preferences of students and teachers:
- Students overwhelmingly prefer "Shark" (90 to 10).
- Teachers have a slight preference for "Moose" (10 to 5).

Therefore, this statement is false.

3. Statement C: "Shark" is more popular with students, but "moose" is more popular with teachers.

To verify this statement:
- Check if "Shark" is more popular with students: Yes, 90 students prefer "Shark", while 10 prefer "Moose".
- Check if "Moose" is more popular with teachers: Yes, 10 teachers prefer "Moose", while only 5 prefer "Shark".

Since both conditions are met, this statement is true.

4. Statement D: "Moose" is more popular with students, but "shark" is more popular with teachers.

To verify this statement:
- Check if "Moose" is more popular with students: No, only 10 students prefer "Moose", while 90 prefer "Shark".
- Although "Shark" is indeed more popular with teachers (5 to 10), the first condition is not met.

Thus, this statement is false.

Based on the above analysis:

- Statement A: True
- Statement B: False
- Statement C: True
- Statement D: False

Thus, the correct statements are A and C.