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?
| | Internet | Not Internet | Total |
|----------|----------|--------------|-------|
| TV | 30 | 5 | 35 |
| Not TV | 11 | 4 | 15 |
| Total | 41 | 9 | 50 |
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's impossible to determine which statement is true based solely on the data from School B's two-way table. Each statement requires a comparison with School A's data, which is currently unavailable.
Explanation
Analyze the problem and data We are given a two-way table summarizing the results of a survey conducted at School B regarding students' TV watching and internet usage habits after finishing homework. We need to compare this data with corresponding data from School A, which is presented in a Venn diagram (not provided). The goal is to determine which of the given statements is true.
Extract data for School B Let's extract the relevant information from the table for School B:
Total students surveyed at School B: 50
Students who do both activities (watch TV and use the internet): 30
Students who watch TV: 35
Students who do neither activity: 4
Represent School A data with variables Since we don't have the Venn diagram for School A, we'll represent the number of students for each category in School A as variables:
Total students surveyed at School A: A_total
Students who do both activities at School A: A_both
Students who watch TV at School A: A_TV
Students who do neither activity at School A: A_neither
Analyze each statement Now, let's analyze each statement and see what information about School A would make the statement true:
Statement 1: More students do both activities at A than at B. This statement is true if 30"> A b o t h > 30 .
Statement 2: More students watch TV at B than at A. This statement is true if A_{TV}"> 35 > A T V , or A T V < 35 .
Statement 3: More students do neither activity at B than at A. This statement is true if A_{neither}"> 4 > A n e i t h er , or A n e i t h er < 4 .
Statement 4: More students were surveyed at A than at B. This statement is true if 50"> A t o t a l > 50 .
Analyze the options and make assumptions Without the Venn diagram for School A, we cannot definitively determine which statement is true. However, we can analyze the options and see if any of them can be eliminated or if we can make a reasonable assumption.
Since we don't have any information about School A, we cannot determine which of the statements is true. However, if we assume that the number of students who do both activities at A is 20, then statement 1 is false. If we assume that the number of students who watch TV at A is 40, then statement 2 is false. If we assume that the number of students who do neither activity at A is 5, then statement 3 is false. If we assume that the number of students surveyed at A is 40, then statement 4 is false.
Therefore, without additional information, we cannot determine which statement is true.
Re-examine the statements Since we don't have the Venn diagram for School A, we cannot definitively determine which statement is true. We need to consider each statement individually and see if we can deduce anything from the given information about School B.
Let's re-examine the statements:
More students do both activities at A than at B. (A > 30)
More students watch TV at B than at A. (35 > A)
More students do neither activity at B than at A. (4 > A)
More students were surveyed at A than at B. (A > 50)
Without knowing the values for School A, we cannot confirm any of these statements.
Final Answer Given the available information, we cannot definitively determine which statement is true without the Venn diagram for School A.
Examples
This type of problem is useful in market research. Imagine two different cities (School A and School B) and you want to understand the media consumption habits of people in those cities. The two-way table and Venn diagram help you compare the number of people who watch TV, use the internet, both, or neither in each city. This information can be used to make decisions about advertising campaigns, such as which media channels to invest in for each city.
Without data from School A, we cannot determine which of the statements A, B, C, or D is true regarding the students' activities at both schools, as all statements require comparison with School A's data.
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