A survey asks teachers and students whether they would like the new school mascot to be a shark or a moose. This table shows the results. Which statement is true?
| | Sharks | Moose | Total |
| :------- | :----- | :---- | :---- |
| Students | 90 | 10 | 100 |
| Teachers | 5 | 10 | 15 |
| Total | 95 | 20 | 115 |
A. "Moose" is equally popular with students and teachers.
B. "Shark" is more popular with students, but "moose" is more popular with teachers.
C. There is no difference between the preferences of students and teachers.
D. "Moose" is more popular with students, but "shark" is more popular with teachers.
Answer (1)
Calculate the proportion of students preferring sharks: 100 90 = 0.9 .
Calculate the proportion of teachers preferring moose: 15 10 = 3 2 ≈ 0.67 .
Compare the preferences: Students prefer sharks, while teachers prefer moose.
The correct statement is: B .
Explanation
Analyze the problem We are given a table that shows the preferences of students and teachers for either a shark or a moose as the new school mascot. We need to determine which statement accurately describes these preferences.
Calculate student preferences First, let's calculate the proportion of students who prefer sharks and moose:
Students who prefer sharks: 90
Students who prefer moose: 10
Total students: 100
Proportion of students preferring sharks: 100 90 = 0.9
Proportion of students preferring moose: 100 10 = 0.1
Calculate teacher preferences Now, let's calculate the proportion of teachers who prefer sharks and moose:
Teachers who prefer sharks: 5
Teachers who prefer moose: 10
Total teachers: 15
Proportion of teachers preferring sharks: 15 5 = 3 1 ≈ 0.33
Proportion of teachers preferring moose: 15 10 = 3 2 ≈ 0.67
Compare preferences Comparing the proportions, we see that:
Students: Sharks (0.9) > Moose (0.1)
Teachers: Moose (0.67) > Sharks (0.33)
This means sharks are more popular with students, while moose are more popular with teachers.
Evaluate statements Now, let's evaluate the given statements:
A. "Moose" is equally popular with students and teachers. - This is false because the proportions are different.
B. "Shark" is more popular with students, but "moose" is more popular with teachers. - This is true based on our calculations.
C. There is no difference between the preferences of students and teachers. - This is false because the proportions are different.
D. "Moose" is more popular with students, but "shark" is more popular with teachers. - This is false because the proportions are opposite.
Final Answer Therefore, the correct statement is B: "Shark" is more popular with students, but "moose" is more popular with teachers.
Examples
Understanding preferences within different groups is crucial in various real-life scenarios. For instance, when a company launches a new product, they survey different demographics to understand which features appeal to each group. This helps them tailor their marketing strategies and product development to maximize appeal and sales across diverse customer segments. Similarly, political campaigns use surveys to gauge voter preferences and adjust their messaging accordingly.
