Watson-Glaser Critical Thinking Appraisal Critical Thinking Appraisal Assessing Probability of Inferences 1

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.

Accepted Answer

The inference is probably true — the controlled trial provides strong but not absolute evidence of a causal link

Answer

The inference is definitely true — the trial data conclusively proves that Vitamin D prevents colds

Answer

The inference is probably false — a correlation observed in a trial does not suggest any real-world effect

Answer

The inference is definitely false — vitamin supplements have no proven effect on viral infections

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.

Accepted Answer

Probably true — the temporal correlation and biological plausibility support the link, though other factors may have contributed

Answer

Definitely true — the timing of the decline after the ban confirms a direct causal relationship

Answer

Probably false — ten years is far too short a time frame for a smoking ban to influence cancer diagnoses

Answer

Definitely false — lung cancer rates are determined entirely by individual genetics, not environmental policy

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.

Accepted Answer

Probably false — the data shows correlation, but higher income may itself enable better sleep conditions, reversing the assumed direction of causality

Answer

Definitely true — adequate sleep is proven to improve cognitive performance and therefore earnings

Answer

Probably true — the large income gap and a plausible biological mechanism confirm the direction of causation

Answer

Definitely false — sleep duration has no measurable relationship to income levels

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.

Accepted Answer

Probably true — the loyalty program is the most plausible explanation, though improved products, marketing, or economic conditions may also have contributed

Answer

Definitely true — the loyalty program was specifically designed to increase repeat visits, and the data confirms it worked

Answer

Probably false — customers rarely alter shopping behavior in response to loyalty programs

Answer

Definitely false — the increase in visits occurred independently of the loyalty program

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.

Accepted Answer

Probably true — the association suggests a positive relationship, although self-selection bias may account for part of the difference

Answer

Definitely true — the 14-percentage-point gap conclusively proves that sports programs drive higher graduation rates

Answer

Probably false — students predisposed to graduate are simply more likely to join sports programs, explaining the entire gap

Answer

Definitely false — extracurricular activities have no measurable impact on academic completion rates

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.

Accepted 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

Answer

Definitely true — the statistics confirm that familiarity with local roads causes drivers to become dangerously overconfident

Answer

Probably true — drivers exercise greater caution in unfamiliar areas, making familiar local driving statistically riskier

Answer

Definitely false — location relative to home has absolutely no bearing on driving safety outcomes