Students from School A and School B were asked whether they watch TV or use the Internet after finishing their homework. The two-way table shows the results from the two surveys. Which statement is true?
A. More students do both activities at A than at B.
B. More students watch TV at B than at A.
C. More students do neither activity at B than at A.
D. More students were surveyed at A than at B.
Answer (2)
Without the Venn diagram for School A, it is impossible to determine which statement is true. The problem requires comparing data from School B with corresponding data from School A, which is missing. Therefore, a definitive answer cannot be provided.
Explanation
Analyze the problem We are given a two-way table for School B showing the number of students who watch TV and use the Internet. We need to compare this data with a Venn diagram for School A, which is not provided. The goal is to determine which of the four given statements is true.
Extract data from School B The table for School B provides the following information:
Students who watch TV and use the Internet: 30
Students who watch TV and do not use the Internet: 5
Students who do not watch TV and use the Internet: 11
Students who do not watch TV and do not use the Internet: 4
Total students surveyed at School B: 50
Analyze each statement Let's analyze each statement based on the data from School B and consider what information we would need from School A to verify the statement.
More students do both activities at A than at B: We need to know the number of students at School A who both watch TV and use the Internet. Let's call this number A b o t h . The statement is true if 30"> A b o t h > 30 .
More students watch TV at B than at A: We need to know the total number of students at School A who watch TV. Let's call this number A T V . The statement is true if A_{TV}"> 35 > A T V .
More students do neither activity at B than at A: We need to know the number of students at School A who do neither activity. Let's call this number A n e i t h er . The statement is true if A_{neither}"> 4 > A n e i t h er .
More students were surveyed at A than at B: We need to know the total number of students surveyed at School A. Let's call this number A t o t a l . The statement is true if 50"> A t o t a l > 50 .
Conclusion Since we don't have the Venn diagram for School A, we cannot definitively determine which statement is true. We need the values A b o t h , A T V , A n e i t h er , and A t o t a l from the Venn diagram to make the comparisons. Without this information, we cannot select a correct answer.
Examples
This type of problem is common in surveys and data analysis. For example, a company might survey its employees to find out how many use certain software programs. The results can be used to make decisions about training and resource allocation. Similarly, schools might survey students to understand their study habits and technology usage, which can inform decisions about curriculum and resource allocation.
Without the data from School A, it is impossible to determine which of the statements about the students and their activities is true. Each statement requires specific numbers from School A for a proper comparison. Thus, we cannot select a correct answer without that information.
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