Items / Reference templates / BP006

REF-BP006-1

C03 independence · C03.1 test independence from table · target medium, CD4 · split test · reference items carry their template's native demand and difficulty

Pending

In a municipal survey, 400 households were classified. Among the 240 rural, 96 subscribe to broadband; among the 160 urban, 64 subscribe to broadband. Is being rural independent of whether a household subscribes to broadband?

ANo, because a household cannot be both rural and urban, so the events are mutually exclusive and therefore dependent.M-INDEP-VS-EXCL
BYes, because the two groups were sampled separately, so their results cannot influence each other.M-INDEP-VS-EXCL
CNo, because P(subscribe to broadband | rural) = 0.4 differs from P(subscribe to broadband) = 0.4.MISC-OTHER
DYes, because P(subscribe to broadband | rural) = 0.4 equals P(subscribe to broadband) = 0.4.Key

Explanation (as written by the item's author)

Independence requires P(subscribe to broadband | rural) = P(subscribe to broadband). Here these are 0.4 and 0.4, so the events are independent.

Distractors and the misconception each claims to execute
Option	Code	Catalogue meaning	Author's rationale
A	M-INDEP-VS-EXCL	Treats mutually exclusive events as independent, or independence as exclusivity.	Confuses mutual exclusivity of the two groups with dependence between the variables.
B	M-INDEP-VS-EXCL	Treats mutually exclusive events as independent, or independence as exclusivity.	Confuses independence of sampling procedure with independence of events.
C	MISC-OTHER	Distractor is not attributable to any catalogued misconception (itself a quality signal).	States the correct comparison but draws the opposite conclusion from it.
D (key)	KEY		Compares the conditional probability with the marginal, which is the definition.

Quality flags · 0 fired

duplicate options (integrity) not firedTwo options are identical after normalisation.
numerically equal options (integrity) not firedTwo options denote the same number (e.g. 0.5 and 1/2 and 50%).
missing options (integrity) not firedFewer than four non-empty options.
key out of range (integrity) not firedThe keyed answer is a probability outside [0, 1] (or a percentage > 100).
all none of above (cue) not firedAn option is 'all/none of the above' or 'both A and B'.
key uniquely longest (cue) not firedThe key is the longest option by at least 20% (length cue).
key uniquely shortest (cue) not firedThe key is the shortest option by at least 20%.
distractor out of range (cue) not firedA distractor is a probability outside [0, 1]; it can be eliminated without the construct.
absolute terms in distractors (cue) not firedDistractors (only) use absolute terms such as always/never/must/proves, a known cue that they are wrong.
stem option overlap cue (cue) not firedThe key alone repeats a content word from the stem.
grammatical mismatch (cue) not firedThe stem ends in 'a'/'an' and some options do not agree with it.
key is hedged only (cue) not firedOnly the key contains hedging language (may/might/plausibly/likely).
numeric middle key (info) not firedOptions are numeric and the key is one of the two middle values. Informational; tested at set level against the 0.5 chance rate.
negative stem (style) not firedStem uses NOT/EXCEPT/LEAST phrasing.
overlong stem (style) not firedStem exceeds 110 words.
inconsistent numeric format (style) not firedNumeric options mix fractions, decimals and percentages, or use differing decimal precision.
unit mismatch (style) not firedOptions carry different units.
option length imbalance (style) not firedLongest option is more than 2.5x the shortest.
rationale value mismatch (metadata) not firedA distractor's stated rationale computes a value ('= x') that is not the option it is attached to: the distractor does not actually execute the misconception it claims.

Validator output

Not a numeric item: no program-of-thought check applies.

Answering probes

Probes not yet run for this item.

Shortcut results

Construct-free heuristics (probability on the key; chance 0.25)
Heuristic	P(key)
longest option	0.00
shortest option	1.00
convergence	1.00
stem overlap	0.33
numeric middle	0.25
hedged option	0.50
position prior	0.00

Provenance and generation trace

Method: reference_template / —
Model: none
Source: parameterised template T-C03.1-indep-table, written by the AssessAI build agent (Claude); no external item bank; not human-reviewed
Prompt hash: —
LLM calls · cost: 0 · $0.00000 · 0.0 s
Parser notes: none