benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 8735 / You have a coin and you would like to check whether it is fair or biased. More…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

You have a coin and you would like to check whether it is fair or biased. More specifically, let θ\theta be the probability of heads, θ=P(H)\theta = P(H). Suppose that you need to choose between the following hypotheses: H_0 (null hypothesis): The coin is fair, i.e. θ=θ0=1/2\theta = \theta_0 = 1 / 2. H_1 (the alternative hypothesis): The coin is not fair, i.e. θ>1/2\theta > 1 / 2. We toss 100 times and observe 60 heads. What is the P-value?
Plain-text mathematical notation (without MathML)
You have a coin and you would like to check whether it is fair or biased. More specifically, let θ be the probability of heads, θ=P(H). Suppose that you need to choose between the following hypotheses: H_0 (null hypothesis): The coin is fair, i.e. θ=θ₀=1/2. H_1 (the alternative hypothesis): The coin is not fair, i.e. θ>1/2. We toss 100 times and observe 60 heads. What is the P-value?
Original LaTeX notation
You have a coin and you would like to check whether it is fair or biased. More specifically, let $\theta$ be the probability of heads, $\theta = P(H)$. Suppose that you need to choose between the following hypotheses: H_0 (null hypothesis): The coin is fair, i.e. $\theta = \theta_0 = 1 / 2$. H_1 (the alternative hypothesis): The coin is not fair, i.e. $\theta > 1 / 2$. We toss 100 times and observe 60 heads. What is the P-value?

category

math

options

  1. 0.115
  2. 0.28
  3. 0.023
  4. 0.157
  5. 0.95
  6. 0.001
  7. 0.5
  8. 0.1
  9. 0.05
  10. 0.082

src

theoremQA-Math

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

upstream_id / Original problem ID
8735
task_id
1eaa50ea-3548-5211-9fcd-b5a2a877ed4f
task_key
default--test--8735
task_revision_id
1
config / split
default / test

Official source

initial import