Practice Exercises: Chapter 7

Group 1: Inductive Strength and Cogency

For each argument, identify if it is Strong or Weak. Then, determine if it is Cogent or Uncogent.

1. “90% of the residents in this city support the expansion of the park. Susan is a resident of this city. Therefore, Susan likely supports the expansion.”

2. “Every time I have dropped a glass on this tile floor, it has shattered. I am about to drop this glass. Therefore, it will probably shatter.”

3. “Two people I know who drive that brand of car have had engine trouble. Therefore, that brand of car is generally unreliable.”

4. “Studies show that nearly all cats are carnivores. My pet, Whiskers, is a cat. Therefore, Whiskers is a carnivore.”

5. “A psychic told me it would rain today. Therefore, I should bring an umbrella because it will probably rain.”

Group 2: Generalization and Sampling

Identify the Target Population, the Sample, and any potential Sampling Errors (Hasty Generalization or Biased Sample).

6. To determine if high school students in the state approve of a new cell phone policy, a researcher polls 500 students at a private preparatory academy.

7. A food critic tastes one bite of a new dish and concludes that the entire menu at the restaurant is substandard.

8. A political pollster calls 1,000 randomly selected registered voters from the national database to estimate the outcome of the presidential election.

9. A gamer asks everyone on their specific Discord server what their favorite console is to determine the most popular console among all gamers worldwide.

Group 3: Probability and Cognitive Biases

Identify which concept or fallacy is at work: Frequentist Probability, Bayesian (Subjective) Probability, Gambler’s Fallacy, or the Base Rate Fallacy.

10. “The last four babies born in this hospital were girls. The next one is almost certainly going to be a boy to even things out.”

11. “I initially thought there was a 50% chance the project would succeed, but after seeing the new budget reports, I’m now 80% sure it will work.”

12. “A test for a very rare condition (1 in 10,000) is 99% accurate. Even though you tested positive, a critical thinker knows the actual probability of having the condition is still low because they consider the background frequency.”

13. “Based on data from the last 50 years, there is a 20% chance of a major flood in this valley during any given decade.”

Group 4: Statistical Pitfalls

Evaluate these scenarios using concepts like Simpson’s Paradox, Mean vs. Median, or Correlation vs. Causation.

14. A company claims the “average” salary is $80,000, but the CEO makes $5 million while most employees make $35,000. Which “average” is the company likely using, and which would be more representative?

15. Hospital A has a higher overall survival rate than Hospital B. However, when looking at specific surgery types (heart, lung, etc.), Hospital B actually has higher survival rates in every category. What is this phenomenon called?

16. Statistics show that ice cream sales and shark attacks both increase during the month of July. Does this mean eating ice cream causes shark attacks?

Answer Key

Group 1

1. Strong and Cogent (High statistical probability; assuming the premise is true).

2. Strong and Cogent (Based on consistent physical observation).

3. Weak and Uncogent (Hasty Generalization; the sample size is far too small).

4. Strong and Cogent (Based on biological fact and high probability).

5. Weak and Uncogent (The source—a psychic—does not provide reliable inductive evidence).

Group 2

6. Target: High school students in the state. Sample: 500 students at a private prep academy. Error: Biased Sample (Students at a private academy may not represent the socio-economic diversity of the whole state).

7. Target: The restaurant’s entire menu. Sample: One bite of one dish. Error: Hasty Generalization.

8. Target: The national voting population. Sample: 1,000 randomly selected voters. Error: None (This is a standard representative random sample).

9. Target: Gamers worldwide. Sample: One specific Discord server. Error: Biased Sample (The server likely attracts a specific niche of gamers).

Group 3

10. Gambler’s Fallacy (Treating independent births as if they have a “memory” of previous outcomes).

11. Bayesian (Subjective) Probability (Updating a degree of belief based on new evidence).

12. Base Rate Fallacy (The “Reasonable Person” avoids this by weighing the test result against the rare base rate).

13. Frequentist Probability (Calculating likelihood based on the observed frequency of historical events).

Group 4

14. They are using the Mean. The Median would be more representative of the “typical” employee because it isn’t skewed by the CEO’s extreme salary.

15. Simpson’s Paradox (Likely caused by Hospital B taking on more “high-risk” cases that lower its aggregate score).

16. Correlation vs. Causation (Both are likely caused by a “lurking variable”—warmer weather leading to more people eating ice cream and more people swimming in the ocean).