A market researcher selected 200 people at random from a group of people who indicated that they liked a certain...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, \(95\%\) said they disliked the movie. Which of the following inferences can appropriately be drawn from this survey result?
At least 95% of people who go see movies will dislike this movie.
At least 95% of people who read books will dislike this movie.
Most people who dislike this book will like this movie.
Most people who like this book will dislike this movie.
1. TRANSLATE the survey setup
- Given information:
- Sample: 200 people selected from those who liked the book
- Action: They watched the movie based on the book
- Result: \(95\%\) disliked the movie
- What this tells us: We have data about people who liked the book and their reaction to the movie
2. INFER the key limitation
- The sample represents only people who liked the book
- Statistical inferences can only be made about the population the sample represents
- Any conclusion must be limited to "people who like the book"
3. INFER which choice matches the sample population
- Choice A: "people who go see movies" - too broad, doesn't match our sample
- Choice B: "people who read books" - too broad, doesn't match our sample
- Choice C: "people who dislike this book" - opposite of our sample population
- Choice D: "people who like this book" - exactly matches our sample population
4. Verify the statistical claim
- Our sample: \(95\%\) of book-likers disliked the movie
- Choice D claims: "Most people who like this book will dislike this movie"
- Since \(95\% \gt 50\%\) ("most"), this inference is supported
Answer: D
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students fail to recognize that statistical inferences are limited by the sample population. They see "\(95\%\)" as a strong result and assume it applies broadly to any related group (moviegoers, book readers, etc.).
This leads them to select Choice A or Choice B, thinking that such a high percentage must generalize to larger populations.
Second Most Common Error:
Poor TRANSLATE reasoning: Students misread or overlook the phrase "from a group of people who indicated that they liked a certain book" and don't realize the sample has this specific limitation.
This causes confusion about what population the results represent, leading to random guessing among the choices.
The Bottom Line:
The key insight is recognizing that statistical samples can only tell us about the population they represent. No matter how strong the results (\(95\%\)!), they cannot be extended beyond the original sample population without additional evidence.
At least 95% of people who go see movies will dislike this movie.
At least 95% of people who read books will dislike this movie.
Most people who dislike this book will like this movie.
Most people who like this book will dislike this movie.