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11 Apr 2024, 22:23
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At least half of the respondents picked "disagree" for at least one question.: Yes
At least one respondent picked "disagree" for Q2 and "somewhat agree" for Q5.: Yes
More than half of the respondents picked "strongly agree" for at least one question.: No
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Difficulty:
35%
(medium)
Question Stats:
79% (01:44) correct
21%
(01:54)
wrong
based on 713
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In a survey, each respondent was asked five questions (Q1 through Q5). The table shows the percentage of respondents who picked each of the four possible responses to the question (strongly agree, agree, somewhat agree, and disagree). For each question, each respondent to the survey picked exactly one of the four possible responses.
For each of the following statements about these survey results, select Yes if the information provided indicates that the statement is correct. Otherwise, select No.
| Response | Q1 | Q2 | Q3 | Q4 | Q5 |
|---|---|---|---|---|---|
| Strongly agree | 15% | 6% | 45% | 15% | 11% |
| Agree | 20% | 18% | 29% | 42% | 13% |
| Somewhat agree | 43% | 24% | 18% | 14% | 55% |
| Disagree | 22% | 52% | 8% | 29% | 21% |
For each of the following statements about these survey results, select Yes if the information provided indicates that the statement is correct. Otherwise, select No.
| Yes | No | |
| At least half of the respondents picked "disagree" for at least one question. | ||
| At least one respondent picked "disagree" for Q2 and "somewhat agree" for Q5. | ||
| More than half of the respondents picked "strongly agree" for at least one question. |
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Official Answer
At least half of the respondents picked "disagree" for at least one question.: Yes
At least one respondent picked "disagree" for Q2 and "somewhat agree" for Q5.: Yes
More than half of the respondents picked "strongly agree" for at least one question.: No
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15 Apr 2024, 20:11
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In a survey, each respondent was asked five questions (Q1 through Q5). The table shows the percentage of respondents who picked each of the four possible responses to the question (strongly agree, agree, somewhat agree, and disagree). For each question, each respondent to the survey picked exactly one of the four possible responses.
(Sort ↕ the table by clicking on the headers)
For each of the following statements about these survey results, select Yes if the information provided indicates that the statement is correct. Otherwise, select No.
At least half of the respondents picked "disagree" for at least one question.
Scanning the table, we see that over half of the respondents, 52%, picked "disagree" for question 2.
Select Yes.
At least one respondent picked "disagree" for Q2 and "somewhat agree" for Q5.
This statement is tricky because table does not tell us what individual respondents picked. So, it may appear that the information provided does not support this statement.
However, notice the following:
Over half of the respondents, 52%, picked "disagree" for Q2, and over half of the respondents picked "somewhat agree" for Q5.
For over half of the respondents to pick two different responses, at least some respondents must pick both of the responses. After all, there's no way for a subset of respondents that's "over half" to be completely different from another subset that's "over half." After all, any subset that includes over half leaves out under half, and under half cannot compose a different subset that's over half.
So, since over half of the respondents picked "disagree" for Q2 and over half picked "somewhat agree" for Q5, at least some picked both responses.
Select Yes.
More than half of the respondents picked "strongly agree" for at least one question.
Scanning the "strongly agree" row, we see that, for all questions, the percentage of respondents who picked "strongly agree" is under 50%.
So, this statement is contrary to what information in the table indicates.
Select No.
Correct answer: Yes, Yes, No
| Response | Q1 | Q2 | Q3 | Q4 | Q5 |
|---|---|---|---|---|---|
| Strongly agree | 15% | 6% | 45% | 15% | 11% |
| Agree | 20% | 18% | 29% | 42% | 13% |
| Somewhat agree | 43% | 24% | 18% | 14% | 55% |
| Disagree | 22% | 52% | 8% | 29% | 21% |
For each of the following statements about these survey results, select Yes if the information provided indicates that the statement is correct. Otherwise, select No.
At least half of the respondents picked "disagree" for at least one question.
Scanning the table, we see that over half of the respondents, 52%, picked "disagree" for question 2.
Select Yes.
At least one respondent picked "disagree" for Q2 and "somewhat agree" for Q5.
This statement is tricky because table does not tell us what individual respondents picked. So, it may appear that the information provided does not support this statement.
However, notice the following:
Over half of the respondents, 52%, picked "disagree" for Q2, and over half of the respondents picked "somewhat agree" for Q5.
For over half of the respondents to pick two different responses, at least some respondents must pick both of the responses. After all, there's no way for a subset of respondents that's "over half" to be completely different from another subset that's "over half." After all, any subset that includes over half leaves out under half, and under half cannot compose a different subset that's over half.
So, since over half of the respondents picked "disagree" for Q2 and over half picked "somewhat agree" for Q5, at least some picked both responses.
Select Yes.
More than half of the respondents picked "strongly agree" for at least one question.
Scanning the "strongly agree" row, we see that, for all questions, the percentage of respondents who picked "strongly agree" is under 50%.
So, this statement is contrary to what information in the table indicates.
Select No.
Correct answer: Yes, Yes, No
17 Apr 2024, 11:01
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Quote:
Since we are looking for the statements to be true, we have to check the stement for all possibilities.
1) At least half of the respondents picked "disagree" for at least one question.
We have to take the worst case scenario that is all those who chose disagree for each question were from same set of people.
The highest % of respondents who disagreed to a particular question was 52%. So, even if the remaining person who disagreed were from tis set of people, there were 52% who disgareed for at least one question.
True
2) At least one respondent picked "disagree" for Q2 and "somewhat agree" for Q5.
In this the worst case would be that there is no or minimal overlap in teh above two categories.
So, 52% disagreed to a particular question Q2 and there were 55% who somewhat agreed to Q5.
Now, the total 100% out of which we take out these 52% and 55% is the same. Even if we take that 100-52% or 48% who did not disagree to the question were part of 55% who some what agreed to Q5, there are 55-48 or 7% left who have to be part of 52%(disagreed Q2 group).
Thus, there is an overlap and the statement is true.
3) More than half of the respondents picked "strongly agree" for at least one question.
The maximum % in strongly agree row is 45%. To take the worst case we take others who disagreed to other Q, 15%(Q1), 6%(Q2), 15%(Q4) and 11%(Q5) to be part of this bigger group 45%.
Thus, it need not be true.
Answer: Y, Y, N
