NBT Academic and Quantitative Literacy Flashcards

A researcher reports that a new study drug reduced migraine frequency by 50% compared to placebo, with a p-value of 0.04. A critic argues the result is clinically insignificant. Which additional piece of information would MOST directly support the critic's position?

Answer: The absolute reduction was from 2 migraines per month to 1 migraine per month across all participants.

Clinical significance differs from statistical significance. A 50% relative reduction sounds impressive, but if the absolute reduction is only 1 migraine per month (from 2 to 1), many clinicians would consider this clinically trivial — especially weighed against potential side effects or costs. This directly supports the 'clinically insignificant' critique. Funding bias (B) raises credibility concerns but not clinical insignificance. The arbitrary p-value cutoff (C) undermines statistical significance, not clinical significance. Small sample size (D) raises concerns about reliability, not clinical meaningfulness.

A municipal water authority publishes a pie chart showing that residential use accounts for 38% of total water consumption, industrial use 41%, agricultural use 17%, and other uses 4%. A council member claims: 'If we cut residential consumption by a quarter, total consumption will fall by nearly 10%.' Evaluate this claim.

Answer: The claim is valid; 25% of 38% equals 9.5%, which is indeed nearly 10%.

The council member's arithmetic is correct: 25% × 38% = 9.5%, which rounds to 'nearly 10%' of total consumption. This is a legitimate proportional calculation. Option B confuses a 25% cut in one sector with eliminating that sector entirely. Option C introduces an irrelevant condition — the calculation is about residential use only. Option D misunderstands the question; relative proportions are sufficient for this calculation even without absolute values.

Read the following argument: 'Studies show that countries with higher chocolate consumption per capita also have more Nobel Prize winners per capita. Therefore, eating chocolate improves cognitive function.' Which logical flaw BEST characterises this argument?

Answer: Conflating correlation with causation while ignoring a confounding variable.

The argument observes a correlation (chocolate consumption and Nobel laureates co-occur in certain countries) and incorrectly infers a causal mechanism. The most plausible explanation is a confounding variable — national wealth — which independently drives both higher chocolate consumption and greater investment in education and research. This is a classic correlation-causation error compounded by a confound. Option B (hasty generalisation) would apply if only one data point were used, but the flaw described is causal, not about sample size. Option C misrepresents circular reasoning. Option D describes a slippery slope, which is not present here.

A table shows monthly loan repayments for a R120 000 loan at 9% per annum, compounded monthly, over different terms: 12 months = R10 464; 24 months = R5 479; 36 months = R3 814; 60 months = R2 490. A borrower wants to minimise the TOTAL interest paid while keeping monthly repayments below R6 000. Which term should they choose?

Answer: 24 months, because it is the shortest term with repayments under R6 000, minimising total interest.

Total interest = (monthly repayment × number of months) − R120 000. For 24 months: R5 479 × 24 = R131 496; interest = R11 496. For 36 months: R3 814 × 36 = R137 304; interest = R17 304. For 60 months: R2 490 × 60 = R149 400; interest = R29 400. The constraint is repayments below R6 000, which rules out the 12-month option (R10 464 > R6 000). Among the remaining options, 24 months minimises total interest paid. Option B and C prioritise cash flow over cost minimisation, which contradicts the objective. Option D ignores the stated repayment constraint.

An academic text states: 'The preponderance of evidence is inimical to the hypothesis that early bilingual exposure attenuates executive function development.' A student summarises this as: 'Most evidence suggests that learning two languages early harms thinking skills.' Assess the student's summary.

Answer: The summary inverts the meaning; 'inimical to the hypothesis' means the evidence opposes the hypothesis that bilingualism attenuates executive function, implying bilingualism does NOT harm development.

Parsing carefully: 'inimical to the hypothesis' means the evidence is hostile/opposed to the hypothesis. The hypothesis being opposed is that bilingual exposure 'attenuates' (weakens/reduces) executive function. So the evidence opposes the idea that bilingualism weakens executive function — meaning the evidence supports bilingualism NOT harming (or even helping) executive function. The student's summary ('harms thinking skills') is the opposite of what the text says. Option B confuses 'inimical to the hypothesis' with 'inimical to the outcome.' Option C is wrong because the direction is not just misrepresented — the entire conclusion is inverted. Option D incorrectly defines 'attenuates.'

A bar graph shows the number of students achieving distinctions in Mathematics at a school over five years: 2019: 24; 2020: 18; 2021: 30; 2022: 27; 2023: 33. The school's total Mathematics enrolment each year was: 2019: 120; 2020: 90; 2021: 150; 2022: 180; 2023: 165. A principal claims: '2023 was our best year for Mathematics distinctions.' Which response MOST accurately evaluates this claim?

Answer: The claim is valid only if measured by absolute numbers; when measured by distinction rate, 2020 was the best year at 20%.

Calculate each year's distinction rate: 2019: 24/120 = 20%; 2020: 18/90 = 20%; 2021: 30/150 = 20%; 2022: 27/180 = 15%; 2023: 33/165 = 20%. All years except 2022 have an identical 20% rate. The principal's claim that 2023 was 'best' is only defensible by raw count (33 distinctions), which is inflated by higher enrolment. By rate, 2020, 2019, 2021, and 2023 all performed equally. Option C correctly identifies that 2020 matched the rate and that absolute counts are what make 2023 appear best — this is the most precise and defensible characterisation. Options A and B contain arithmetic errors or imprecise reasoning. Option D singles out 2019 without noting that other years matched it.