Texting behavior vs Talks on cell phone daily/Does not talk on cell phone daily:Texting behaviorTalks on cell phone dailyDoes not...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
Texting behavior vs Talks on cell phone daily/Does not talk on cell phone daily:
| Texting behavior | Talks on cell phone daily | Does not talk on cell phone daily | Total |
|---|---|---|---|
| Light | 110 | 146 | 256 |
| Medium | 139 | 164 | 303 |
| Heavy | 166 | 74 | 240 |
| Total | 415 | 384 | 799 |
In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table above. Based on the data from the study, an estimate of the percent of US teens who are heavy texters is \(30\%\) and the associated margin of error is \(3\%\). Which of the following is a correct statement based on the given margin of error?
Approximately 3% of the teens in the study who are classified as heavy texters are not really heavy texters.
It is not possible that the percent of all US teens who are heavy texters is less than 27%.
The percent of all US teens who are heavy texters is 33%.
It is doubtful that the percent of all US teens who are heavy texters is 35%.
1. TRANSLATE the statistical information
- Given information:
- Estimate: \(30\%\) of US teens are heavy texters
- Margin of error: \(3\%\)
- Need to evaluate statements about what this means
2. INFER what margin of error means
- Margin of error creates a confidence interval around the estimate
- The true population percentage is likely within: \(30\% \pm 3\%\)
- This gives us the interval: \(27\%\) to \(33\%\)
3. APPLY CONSTRAINTS to evaluate each choice
- Choice A: Margin of error doesn't tell us about misclassification within the study
- Choice B: Says "not possible" to be below \(27\%\) - too strong, it's just unlikely
- Choice C: Claims the percentage "is \(33\%\)" - but any value in \(27\%\) to \(33\%\) is equally likely
- Choice D: Claims it's "doubtful" the percentage is \(35\%\) - since \(35\%\) is outside our interval, this is correct
Answer: D
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students don't understand what margin of error actually means. They might think it refers to measurement error in the study itself rather than uncertainty about the true population parameter.
This confusion leads them to misinterpret Choice A as correct, thinking the \(3\%\) margin of error means \(3\%\) of students were misclassified in the study.
Second Most Common Error:
Poor APPLY CONSTRAINTS reasoning: Students understand the confidence interval concept but don't properly apply it to evaluate the answer choices. They might choose Choice B because they think "not possible" and "unlikely" mean the same thing statistically.
This leads them to select Choice B instead of recognizing that statistical confidence intervals allow for possibilities outside the range, just with low probability.
The Bottom Line:
This problem tests whether students understand that margin of error creates a range of likely values for the true population parameter, not a statement about data quality or measurement precision within the study itself.
Approximately 3% of the teens in the study who are classified as heavy texters are not really heavy texters.
It is not possible that the percent of all US teens who are heavy texters is less than 27%.
The percent of all US teens who are heavy texters is 33%.
It is doubtful that the percent of all US teens who are heavy texters is 35%.