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MMLU-Pro / 8537 / 7.4-15. If (X)¯ and (Y)¯ are the respective means of two independent…

Problem

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question

7.4-15. If X¯\bar{X} and Y¯\bar{Y} are the respective means of two independent random samples of the same size nn, find nn if we want x¯−y¯±4\bar{x}-\bar{y} \pm 4 to be a 90%90 \% confidence interval for μX−μY\mu_X-\mu_Y. Assume that the standard deviations are known to be σX=15\sigma_X=15 and σY=25\sigma_Y=25.
Plain-text mathematical notation (without MathML)
7.4-15. If (X)¯ and (Y)¯ are the respective means of two independent random samples of the same size n, find n if we want (x)¯−(y)¯±4 to be a 90% confidence interval for μ_(X)−μ_(Y). Assume that the standard deviations are known to be σ_(X)=15 and σ_(Y)=25.
Original LaTeX notation
7.4-15. If $\bar{X}$ and $\bar{Y}$ are the respective means of two independent random samples of the same size $n$, find $n$ if we want $\bar{x}-\bar{y} \pm 4$ to be a $90 \%$ confidence interval for $\mu_X-\mu_Y$. Assume that the standard deviations are known to be $\sigma_X=15$ and $\sigma_Y=25$.

category

math

options

  1. 180
  2. $144$
  3. 120
  4. 210
  5. 100
  6. 150
  7. 170
  8. 130
  9. 160
  10. 200

src

scibench-stat

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Source and history

upstream_id / Original problem ID
8537
task_id
cf6c0fea-6acc-50a1-82c4-b81e9558a744
task_key
default--test--8537
task_revision_id
1
config / split
default / test

Official source

initial import