Watson-Glaser Critical Thinking Appraisal Critical Thinking Appraisal Assessing Probability of Inferences 1 — Questions and Answers
Question 1: A pharmaceutical company conducted a randomized controlled trial in which participants who took daily Vitamin D supplements reported 30% fewer colds over six months compared to the placebo group. What is the probability of the following inference: Vitamin D supplementation reduces the frequency of colds.
- The inference is definitely true — the trial data conclusively proves that Vitamin D prevents colds
- The inference is probably true — the controlled trial provides strong but not absolute evidence of a causal link (Correct answer)
- The inference is probably false — a correlation observed in a trial does not suggest any real-world effect
- The inference is definitely false — vitamin supplements have no proven effect on viral infections
Correct answer: The inference is probably true — the controlled trial provides strong but not absolute evidence of a causal link
A randomized controlled trial showing a 30% reduction provides meaningful evidence, making the inference probably true. However, a single trial can have sample-size limitations, undisclosed confounders, or industry bias, so the inference cannot be elevated to 'definitely true.'
Question 2: A city that banned smoking in all public indoor spaces saw its lung cancer diagnosis rate fall by 25% over the following decade. What is the probability of the following inference: The public smoking ban directly caused the decline in lung cancer rates.
- Definitely true — the timing of the decline after the ban confirms a direct causal relationship
- Probably true — the temporal correlation and biological plausibility support the link, though other factors may have contributed (Correct answer)
- Probably false — ten years is far too short a time frame for a smoking ban to influence cancer diagnoses
- Definitely false — lung cancer rates are determined entirely by individual genetics, not environmental policy
Correct answer: Probably true — the temporal correlation and biological plausibility support the link, though other factors may have contributed
The temporal sequence and well-established biology (reduced smoke exposure → reduced cancer risk) make the inference probably true, but advances in early detection, concurrent anti-smoking campaigns, or demographic shifts could also partly explain the decline, preventing a 'definitely true' rating.
Question 3: A national survey of 500 employed adults found that those who sleep 7–9 hours per night earn on average $15,000 more annually than those who sleep fewer than 6 hours per night. What is the probability of the following inference: Getting adequate sleep will increase a person's annual income.
- Definitely true — adequate sleep is proven to improve cognitive performance and therefore earnings
- Probably true — the large income gap and a plausible biological mechanism confirm the direction of causation
- Probably false — the data shows correlation, but higher income may itself enable better sleep conditions, reversing the assumed direction of causality (Correct answer)
- Definitely false — sleep duration has no measurable relationship to income levels
Correct answer: Probably false — the data shows correlation, but higher income may itself enable better sleep conditions, reversing the assumed direction of causality
The inference assumes sleep causes higher income, but the causal arrow may run the other way: higher-income individuals may have less stressful, more flexible jobs that allow adequate sleep. Survey data alone cannot establish which variable drives the other.
Question 4: A retail chain introduced a points-based customer loyalty program in January. By December of the same year, repeat customer visits had increased by 35% compared to the prior year. What is the probability of the following inference: The loyalty program caused the increase in repeat customer visits.
- Definitely true — the loyalty program was specifically designed to increase repeat visits, and the data confirms it worked
- Probably true — the loyalty program is the most plausible explanation, though improved products, marketing, or economic conditions may also have contributed (Correct answer)
- Probably false — customers rarely alter shopping behavior in response to loyalty programs
- Definitely false — the increase in visits occurred independently of the loyalty program
Correct answer: Probably true — the loyalty program is the most plausible explanation, though improved products, marketing, or economic conditions may also have contributed
The loyalty program is the most salient change and aligns logically with the outcome, making the inference probably true. However, without a control group or isolation of other variables (new store locations, advertising spend, seasonal trends), certainty is not justified.
Question 5: A national study found that students who participate in after-school sports programs graduate high school at a rate of 92%, compared to a 78% graduation rate for non-participants. What is the probability of the following inference: After-school sports programs increase the likelihood of high school graduation.
- Definitely true — the 14-percentage-point gap conclusively proves that sports programs drive higher graduation rates
- Probably true — the association suggests a positive relationship, although self-selection bias may account for part of the difference (Correct answer)
- Probably false — students predisposed to graduate are simply more likely to join sports programs, explaining the entire gap
- Definitely false — extracurricular activities have no measurable impact on academic completion rates
Correct answer: Probably true — the association suggests a positive relationship, although self-selection bias may account for part of the difference
Sports programs plausibly support graduation through structured routines, adult mentorship, and school engagement, making the inference probably true. However, self-selection bias — motivated, academically oriented students are more likely to join sports — means the full 14-point gap cannot be attributed solely to program participation.
Question 6: An analysis of 1,000 car accidents in a metropolitan area found that 68% occurred within 15 miles of the driver's home address. What is the probability of the following inference: Driving close to home is more dangerous than driving in unfamiliar areas.
- Definitely true — the statistics confirm that familiarity with local roads causes drivers to become dangerously overconfident
- Probably true — drivers exercise greater caution in unfamiliar areas, making familiar local driving statistically riskier
- Probably false — the data most likely reflects that the majority of all driving occurs near home, making local accidents more frequent without indicating greater risk per mile driven (Correct answer)
- Definitely false — location relative to home has absolutely no bearing on driving safety outcomes
Correct answer: Probably false — the data most likely reflects that the majority of all driving occurs near home, making local accidents more frequent without indicating greater risk per mile driven
This is a base-rate error: most people's total driving miles are accumulated near their home, so accidents naturally cluster there by volume, not by elevated risk. Without knowing miles driven per zone, the accident count alone does not establish that local driving is more dangerous per mile.
Watson-Glaser Critical Thinking Appraisal Critical Thinking Appraisal Assessing Probability of Inferences 1
A pharmaceutical company conducted a randomized controlled trial in which participants who took daily Vitamin D supplements reported 30% fewer colds over six months compared to the placebo group.
What is the probability of the following inference: Vitamin D supplementation reduces the frequency of colds.