prompt
dict | response
string | meta
dict | fact_sources
list | artifacts
dict |
|---|---|---|---|---|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Verify TRUE/FALSE and correct if false: A p-value is the probability that the null hypothesis is true."
}
]
}
|
FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
|
{
"id": "WUA_STAT_25K_000001",
"domain": "master_scholars_academics",
"subdomain": "stats::hypothesis_testing",
"task": "fact_check",
"difficulty": "advanced",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Verify TRUE/FALSE and correct if false: Correlation implies causation."
}
]
}
|
FALSE — Correlation alone does not establish causation.
|
{
"id": "WUA_STAT_25K_000002",
"domain": "master_scholars_academics",
"subdomain": "stats::modeling",
"task": "fact_check",
"difficulty": "advanced",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "True or False (academics): A p-value is the probability that the null hypothesis is true."
}
]
}
|
FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
|
{
"id": "WUA_STAT_25K_000003",
"domain": "master_scholars_academics",
"subdomain": "stats::hypothesis_testing",
"task": "fact_check",
"difficulty": "seed",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Verify TRUE/FALSE and correct if false: The standard deviation is the square root of the variance."
}
]
}
|
TRUE — The standard deviation is the square root of the variance.
|
{
"id": "WUA_STAT_25K_000004",
"domain": "master_scholars_academics",
"subdomain": "stats::distribution",
"task": "fact_check",
"difficulty": "advanced",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "True or False (academics): The standard deviation is the square root of the variance."
}
]
}
|
TRUE — The standard deviation is the square root of the variance.
|
{
"id": "WUA_STAT_25K_000005",
"domain": "master_scholars_academics",
"subdomain": "stats::distribution",
"task": "fact_check",
"difficulty": "seed",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Verify TRUE/FALSE and correct if false: A p-value is the probability that the null hypothesis is true."
}
]
}
|
FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
|
{
"id": "WUA_STAT_25K_000006",
"domain": "master_scholars_academics",
"subdomain": "stats::hypothesis_testing",
"task": "fact_check",
"difficulty": "core",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Verify TRUE/FALSE and correct if false: Independence means P(A∩B) = P(A)P(B)."
}
]
}
|
TRUE — Independence means P(A∩B) = P(A)P(B).
|
{
"id": "WUA_STAT_25K_000007",
"domain": "master_scholars_academics",
"subdomain": "stats::probability",
"task": "fact_check",
"difficulty": "advanced",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Verify TRUE/FALSE and correct if false: Independence means P(A∩B) = P(A)P(B)."
}
]
}
|
TRUE — Independence means P(A∩B) = P(A)P(B).
|
{
"id": "WUA_STAT_25K_000008",
"domain": "master_scholars_academics",
"subdomain": "stats::probability",
"task": "fact_check",
"difficulty": "core",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "True or False (academics): A p-value is the probability that the null hypothesis is true."
}
]
}
|
FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
|
{
"id": "WUA_STAT_25K_000009",
"domain": "master_scholars_academics",
"subdomain": "stats::hypothesis_testing",
"task": "fact_check",
"difficulty": "advanced",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "True or False (academics): A probability must lie between 0 and 1 inclusive."
}
]
}
|
TRUE — A probability must lie between 0 and 1 inclusive.
|
{
"id": "WUA_STAT_25K_000010",
"domain": "master_scholars_academics",
"subdomain": "stats::probability",
"task": "fact_check",
"difficulty": "advanced",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "True or False (academics): Independence means P(A∩B) = P(A)P(B)."
}
]
}
|
TRUE — Independence means P(A∩B) = P(A)P(B).
|
{
"id": "WUA_STAT_25K_000011",
"domain": "master_scholars_academics",
"subdomain": "stats::probability",
"task": "fact_check",
"difficulty": "advanced",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Verify TRUE/FALSE and correct if false: The standard deviation is the square root of the variance."
}
]
}
|
TRUE — The standard deviation is the square root of the variance.
|
{
"id": "WUA_STAT_25K_000012",
"domain": "master_scholars_academics",
"subdomain": "stats::distribution",
"task": "fact_check",
"difficulty": "core",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Verify TRUE/FALSE and correct if false: A probability must lie between 0 and 1 inclusive."
}
]
}
|
TRUE — A probability must lie between 0 and 1 inclusive.
|
{
"id": "WUA_STAT_25K_000013",
"domain": "master_scholars_academics",
"subdomain": "stats::probability",
"task": "fact_check",
"difficulty": "core",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "True or False (academics): A p-value is the probability that the null hypothesis is true."
}
]
}
|
FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
|
{
"id": "WUA_STAT_25K_000014",
"domain": "master_scholars_academics",
"subdomain": "stats::hypothesis_testing",
"task": "fact_check",
"difficulty": "core",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Academic fact-check: TRUE/FALSE then corrected statement if needed: The standard deviation is the square root of the variance."
}
]
}
|
TRUE — The standard deviation is the square root of the variance.
|
{
"id": "WUA_STAT_25K_000015",
"domain": "master_scholars_academics",
"subdomain": "stats::distribution",
"task": "fact_check",
"difficulty": "seed",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Academic fact-check: TRUE/FALSE then corrected statement if needed: A p-value is the probability that the null hypothesis is true."
}
]
}
|
FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
|
{
"id": "WUA_STAT_25K_000016",
"domain": "master_scholars_academics",
"subdomain": "stats::hypothesis_testing",
"task": "fact_check",
"difficulty": "seed",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Verify TRUE/FALSE and correct if false: A p-value is the probability that the null hypothesis is true."
}
]
}
|
FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
|
{
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — Independence means P(A∩B) = P(A)P(B).
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FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — The standard deviation is the square root of the variance.
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FALSE — Correlation alone does not establish causation.
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FALSE — Correlation alone does not establish causation.
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TRUE — A probability must lie between 0 and 1 inclusive.
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FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — A probability must lie between 0 and 1 inclusive.
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — The standard deviation is the square root of the variance.
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — A probability must lie between 0 and 1 inclusive.
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TRUE — A probability must lie between 0 and 1 inclusive.
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FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
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TRUE — The standard deviation is the square root of the variance.
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FALSE — Correlation alone does not establish causation.
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FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
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TRUE — A probability must lie between 0 and 1 inclusive.
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FALSE — Correlation alone does not establish causation.
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FALSE — Correlation alone does not establish causation.
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TRUE — The standard deviation is the square root of the variance.
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TRUE — The standard deviation is the square root of the variance.
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TRUE — Independence means P(A∩B) = P(A)P(B).
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FALSE — Correlation alone does not establish causation.
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TRUE — Independence means P(A∩B) = P(A)P(B).
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FALSE — Correlation alone does not establish causation.
|
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TRUE — The standard deviation is the square root of the variance.
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TRUE — Independence means P(A∩B) = P(A)P(B).
|
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TRUE — Independence means P(A∩B) = P(A)P(B).
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FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — A probability must lie between 0 and 1 inclusive.
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{
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TRUE — Independence means P(A∩B) = P(A)P(B).
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TRUE — Independence means P(A∩B) = P(A)P(B).
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{
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FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
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{
"role": "user",
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FALSE — Correlation alone does not establish causation.
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FALSE — A p-value is P(data as or more extreme | null), not P(null | data).
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] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "Academic fact-check: TRUE/FALSE then corrected statement if needed: Correlation implies causation."
}
]
}
|
FALSE — Correlation alone does not establish causation.
|
{
"id": "WUA_STAT_25K_000099",
"domain": "master_scholars_academics",
"subdomain": "stats::modeling",
"task": "fact_check",
"difficulty": "seed",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
{
"messages": [
{
"role": "system",
"content": "You are WithinUsAI Master Scholars Statistics. Provide concise, factual answers."
},
{
"role": "user",
"content": "True or False (academics): Independence means P(A∩B) = P(A)P(B)."
}
]
}
|
TRUE — Independence means P(A∩B) = P(A)P(B).
|
{
"id": "WUA_STAT_25K_000100",
"domain": "master_scholars_academics",
"subdomain": "stats::probability",
"task": "fact_check",
"difficulty": "core",
"truth_mode": "verifiable_fact",
"wrapper": "verify_true_false",
"created_utc": "2026-01-04T05:02:58",
"license": "cc-by-4.0",
"tags": [
"statistics",
"academics",
"verification"
]
}
|
[
{
"source_title": "OpenStax Introductory Statistics (CC BY 4.0)",
"source_url": "https://openstax.org/details/books/introductory-statistics",
"evidence_type": "standard",
"accessed_at_utc": "2026-01-04T05:02:58"
},
{
"source_title": "NIST/SEMATECH e-Handbook of Statistical Methods",
"source_url": "https://www.itl.nist.gov/div898/handbook/",
"evidence_type": "official",
"accessed_at_utc": "2026-01-04T05:02:58"
}
] |
{
"max_tokens_hint": 220,
"style_contract": "concise_formal"
}
|
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