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MMLU-Pro / 7795 / Which of these explains why t should be used instead of z for inference…

Problem

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question

Which of these explains why t should be used instead of z for inference procedures for means.

category

math

options

  1. The use of t instead of z is simply a convention in statistics, with no mathematical reason.
  2. The Central Limit Theorem applies to means but not proportions.
  3. We use z for proportions because proportions are approximately normal. Means are not.
  4. We use z for proportions because the sampling distribution of sample proportions is approximately normal, but that is not the case for the sampling distribution of sample means.
  5. We use t for means because the sampling distribution of sample means is approximately normal, but that is not the case for proportions.
  6. When using the sample standard deviation to estimate the population standard deviation, more variability is introduced into the sampling distribution of the statistic.
  7. The Central Limit Theorem applies to proportions but not means.
  8. We use t for means because it provides a more accurate estimate of the population mean.

src

ori_mmlu-high_school_statistics

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Source and history

upstream_id / Original problem ID
7795
task_id
28d82ec2-edd4-540d-9f9f-9f95164796c8
task_key
default--test--7795
task_revision_id
1
config / split
default / test

Official source

initial import