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MMLU-Pro / 8544 / The principal of a school is interested in estimating the average income per…

Problem

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question

The principal of a school is interested in estimating the average income per family of her students. She selects a random sample of students and collects information about their family income. A 95 percent confidence interval computed from this data for the mean income per family is (35,095,35,095, 45,005). Which of the following provides the best interpretation of this confidence interval?
Plain-text mathematical notation (without MathML)
The principal of a school is interested in estimating the average income per family of her students. She selects a random sample of students and collects information about their family income. A 95 percent confidence interval computed from this data for the mean income per family is (35,095,45,005). Which of the following provides the best interpretation of this confidence interval?
Original LaTeX notation
The principal of a school is interested in estimating the average income per family of her students. She selects a random sample of students and collects information about their family income. A 95 percent confidence interval computed from this data for the mean income per family is ($35,095, $45,005). Which of the following provides the best interpretation of this confidence interval?

category

math

options

  1. 95 percent of the students in her school are from families whose income is between $35,095 and $45,005.
  2. If we were to take another sample of the same size and compute a 95 percent confidence interval, we would have a 95% chance of getting a different interval.
  3. If we were to take another sample of the same size and compute a 95 percent confidence interval, we would have a 95% chance of getting the interval ($35,095, $45,005).
  4. There is a 95% probability that the mean income per family in the school is between $35,095 and $45,005.
  5. 95 percent of the income per family in the school falls between $35,095 and $45,005.
  6. There is a 95% probability that the median income per family in the school is between $35,095 and $45,005.
  7. There is a 95% probability that the sample mean income per family in the school is between $35,095 and $45,005.
  8. The average income per family of all the students in the school is definitely between $35,095 and $45,005.
  9. There is a 95% probability that the minimum income per family in the school is between $35,095 and $45,005.
  10. There is a 95% probability that the families of all the students in this school have an income of between $35,095 and $45,005.

src

ori_mmlu-high_school_statistics

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Source and history

upstream_id / Original problem ID
8544
task_id
cc8652ca-6e7f-5165-99dc-ecf54157ddd5
task_key
default--test--8544
task_revision_id
1
config / split
default / test

Official source

initial import