CCTST Inference 3 — Questions and Answers
Question 1: A researcher notices that regions with higher literacy rates also have lower infant mortality. The most cautious inference is:
- Teaching people to read will immediately lower infant mortality.
- Literacy and infant mortality are inversely correlated. (Correct answer)
- Illiterate mothers cause infant deaths.
- Infant mortality causes lower literacy rates.
Correct answer: Literacy and infant mortality are inversely correlated.
Observational data establish a relationship between the two variables but cannot on their own prove causation or direction.
Question 2: A coin is flipped ten times and lands heads each time. What is the best inference about the eleventh flip?
- It will almost certainly land tails to balance out.
- It will almost certainly land heads again.
- The probability of heads on the next flip remains approximately 50% for a fair coin. (Correct answer)
- The coin must be unfair.
Correct answer: The probability of heads on the next flip remains approximately 50% for a fair coin.
For a fair coin, each flip is independent, so past results do not change the probability of future outcomes.
Question 3: A news article states that a new drug reduced symptoms in 70% of trial participants. What is the most warranted inference?
- The drug will eliminate the disease within a decade.
- The drug was effective for a majority of participants in the trial. (Correct answer)
- Everyone who takes the drug will benefit.
- The drug has no side effects.
Correct answer: The drug was effective for a majority of participants in the trial.
The stated statistic only justifies concluding that most trial participants experienced symptom reduction.
Question 4: Tom says, 'Every time I wash my car, it rains.' From this statement alone, what can be inferred?
- Washing the car causes rain.
- Tom has observed a coincidental pattern that he has not causally explained. (Correct answer)
- Tom should stop washing his car.
- Rain damages car washes.
Correct answer: Tom has observed a coincidental pattern that he has not causally explained.
Tom is describing a perceived pattern, but the statement provides no causal mechanism linking car washing to precipitation.
Question 5: An advertisement claims 'four out of five dentists recommend SparkleBright toothpaste.' Which inference is best supported?
- SparkleBright is the best toothpaste available.
- The fifth dentist recommends no toothpaste.
- In the survey cited, 80% of dentists recommended SparkleBright. (Correct answer)
- All dentists agree on which toothpaste is best.
Correct answer: In the survey cited, 80% of dentists recommended SparkleBright.
The claim only justifies inferring that 80% of dentists in the cited survey gave that recommendation; no broader conclusion is warranted.
Question 6: Premises: 'If it snows, school is canceled. It did not snow.' What can be inferred?
- School was not canceled.
- School was definitely in session.
- Nothing can be determined about whether school was canceled. (Correct answer)
- It must have rained instead.
Correct answer: Nothing can be determined about whether school was canceled.
The absence of snow only tells us the sufficient condition for cancellation was not met; school could still be canceled for other reasons.
Question 7: A student scores in the 90th percentile on a standardized test. What does this most accurately indicate?
- The student answered 90% of questions correctly.
- The student scored higher than 90% of test takers. (Correct answer)
- The student will perform well in college.
- The test was easy for this student.
Correct answer: The student scored higher than 90% of test takers.
A percentile rank indicates relative standing among test takers, not a percentage of questions answered correctly.
CCTST Inference 3
A researcher notices that regions with higher literacy rates also have lower infant mortality.
The most cautious inference is: