Watson Statistical Reasoning and Sampling

Question 1

A survey of 50 university students finds that 80% prefer online learning. A newspaper headline reads: 'Most people prefer online learning.' What is the main flaw in this conclusion?

Accepted Answer

The sample is too small and too specific to represent the general population

Answer

University students are a narrow, self-selected group whose preferences are unlikely to reflect those of the broader population. Both the small sample size and the lack of representativeness undermine the generalization. A valid conclusion would need a larger, diverse, randomly selected sample.

Question 2

A study finds that cities with more libraries have higher average incomes. A researcher concludes that 'building more libraries increases income.' What is wrong with this reasoning?

Accepted Answer

The researcher has confused correlation with causation

Answer

Correlation — two variables moving together — does not establish that one causes the other. A third factor (e.g., wealthier cities can afford both more libraries and higher wages) could explain the relationship. Causal claims require evidence beyond statistical association.

Question 3

Drug A reduced symptoms in 60% of 10 trial participants. Drug B reduced symptoms in 55% of 1,000 trial participants. Which result provides stronger evidence of effectiveness?

Accepted Answer

Drug B, because its larger sample produces a more reliable estimate

Answer

With only 10 participants, Drug A's 60% result (6 people) could easily be due to chance. Drug B's result from 1,000 participants is statistically far more stable and reliable. A larger sample reduces random variation, making the percentage estimate more trustworthy even if slightly lower.

Question 4

A company surveys employees by placing a feedback form on the staff intranet. 90% of respondents say they are satisfied with management. Why should this result be interpreted cautiously?

Accepted Answer

Only motivated respondents self-select into the survey, creating a biased sample

Answer

Self-selection bias occurs when participation is voluntary — those with strong positive feelings (or strong negative feelings) are more likely to respond than those with moderate views. The sample therefore does not represent all employees, making it impossible to generalize the 90% figure to the full workforce.

Question 5

A clinical study reports that a new therapy reduces anxiety scores by an average of 15 points. The study notes a standard deviation of 18 points. What does the high standard deviation indicate?

Accepted Answer

The 15-point average conceals wide variation in individual responses

Answer

A standard deviation larger than the mean improvement signals that outcomes varied enormously: some participants improved far more than 15 points, others barely at all or worsened. Reporting only the average without this context would overstate the therapy's predictable benefit for any given individual.

Watson-Glaser Critical Thinking Appraisal Practice Test

Watson-Glaser Critical Thinking Appraisal Practice Test

Watson Statistical Reasoning and Sampling