Let's analyze the problem step-by-step to determine the correct statement.
### Step 1: Understand the data
We have the following data from a survey on preferences for a new school mascot:
- 90 students prefer sharks.
- 10 students prefer moose.
- 5 teachers prefer sharks.
- 10 teachers prefer moose.
### Step 2: Calculate the total number of students and teachers
- Total students: [tex]\( 90 + 10 = 100 \)[/tex]
- Total teachers: [tex]\( 5 + 10 = 15 \)[/tex]
### Step 3: Calculate the proportions
We need to determine the proportion of students and teachers who prefer each mascot.
- Proportion of students preferring sharks: [tex]\( \frac{90}{100} = 0.90 \)[/tex]
- Proportion of students preferring moose: [tex]\( \frac{10}{100} = 0.10 \)[/tex]
- Proportion of teachers preferring sharks: [tex]\( \frac{5}{15} \approx 0.33 \)[/tex]
- Proportion of teachers preferring moose: [tex]\( \frac{10}{15} \approx 0.67 \)[/tex]
### Step 4: Evaluate the statements
Let's analyze each statement based on our calculated proportions.
Statement A: "Moose" is equally popular with students and teachers.
- Proportion of students preferring moose: [tex]\( 0.10 \)[/tex]
- Proportion of teachers preferring moose: [tex]\( 0.67 \)[/tex]
- These proportions are not equal, so Statement A is false.
Statement B: "Shark" is more popular with students, but "moose" is more popular with teachers.
- Proportion of students preferring sharks [tex]\( 0.90 \)[/tex] is greater than proportion of students preferring moose [tex]\( 0.10 \)[/tex].
- Proportion of teachers preferring moose [tex]\( 0.67 \)[/tex] is greater than proportion of teachers preferring sharks [tex]\( 0.33 \)[/tex].
- This statement is true based on our proportions.
Statement C: There is no difference between the preferences of students and teachers.
- The proportions for both groups are different (students greatly prefer sharks and teachers prefer moose), so Statement C is false.
Statement D: "Moose" is more popular with students, but "shark" is more popular with teachers.
- Proportion of students preferring moose [tex]\( 0.10 \)[/tex] is not greater than proportion of students preferring sharks [tex]\( 0.90 \)[/tex].
- Proportion of teachers preferring sharks [tex]\( 0.33 \)[/tex] is not greater than proportion of teachers preferring moose [tex]\( 0.67 \)[/tex].
- This statement is false.
### Conclusion
Based on our analysis, the correct statement is:
B. "Shark" is more popular with students, but "moose" is more popular with teachers.
