CCTST Inductive Reasoning 5 — Questions and Answers
Question 1: In a statistical syllogism, the argument form is: 'X% of F are G; a is F; therefore, a is probably G.' This argument is stronger when:
- X is close to 50%
- X is very high or very low (Correct answer)
- The conclusion is universal
- G is a rare property
Correct answer: X is very high or very low
Statistical syllogisms are stronger when the percentage is far from 50%, giving clearer probabilistic support for the conclusion.
Question 2: Which of the following is an example of hasty generalization?
- Concluding the sun will rise tomorrow based on millions of prior observations
- Concluding all teenagers are irresponsible after one teenager makes a mistake (Correct answer)
- Inferring that a new drug works after 1,000 controlled clinical trials
- Arguing that most birds fly because 99% of observed birds fly
Correct answer: Concluding all teenagers are irresponsible after one teenager makes a mistake
Hasty generalization draws a sweeping conclusion from an insufficient number of cases.
Question 3: Which principle best explains why inductive conclusions can never be proven with absolute certainty?
- The principle of non-contradiction
- Hume's problem of induction (Correct answer)
- The law of excluded middle
- Gödel's incompleteness theorem
Correct answer: Hume's problem of induction
Hume's problem of induction shows that past observations cannot logically guarantee future events, making certainty impossible.
Question 4: A public health official observes that neighborhoods with more fast-food restaurants have higher obesity rates. To establish a causal claim inductively, the next best step is:
- Assume the correlation proves causation
- Control for confounding variables like income and exercise habits (Correct answer)
- Reduce the number of neighborhoods studied
- Switch to a deductive argument
Correct answer: Control for confounding variables like income and exercise habits
Controlling for confounding variables is essential to move from a mere correlation toward a defensible causal conclusion.
Question 5: A wine expert correctly identifies grape varieties in 95 out of 100 blind tastings. An observer concludes the expert can reliably distinguish grape varieties by taste. This inductive argument is:
- Weak because 5 errors occurred
- Strong because the sample is large and the success rate is very high (Correct answer)
- Invalid because wine tasting is subjective
- Cogent only if the expert has a degree
Correct answer: Strong because the sample is large and the success rate is very high
A 95% success rate across 100 trials constitutes strong inductive evidence for the expert's ability.
Question 6: When evaluating an inductive argument on the CCTST, which question is MOST relevant?
- Does the conclusion follow necessarily from the premises?
- Are the premises logically consistent with each other?
- Do the premises make the conclusion more likely to be true? (Correct answer)
- Is the argument expressed in standard logical form?
Correct answer: Do the premises make the conclusion more likely to be true?
Inductive evaluation focuses on whether premises raise the probability that the conclusion is true, not whether it follows necessarily.
Question 7: Which of the following best describes the relationship between evidence quantity and inductive argument strength?
- More evidence always makes an argument deductively valid
- More representative evidence generally increases inductive strength (Correct answer)
- Quantity of evidence is irrelevant to inductive strength
- More evidence always guarantees a true conclusion
Correct answer: More representative evidence generally increases inductive strength
Greater quantities of representative evidence typically increase the probability that an inductive conclusion is correct.
CCTST Inductive Reasoning 5
In a statistical syllogism, the argument form is: 'X% of F are G; a is F; therefore, a is probably G.' This argument is stronger when: