An analyst collected data on the price of a carton of grape tomatoes at 30 locations selected at random in...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
An analyst collected data on the price of a carton of grape tomatoes at 30 locations selected at random in Utah. The mean price of a carton of grape tomatoes in Utah was estimated to be \(\$4.23\), with an associated margin of error of \(\$0.08\). Which of the following is a plausible statement about the mean price of a carton of grape tomatoes for all locations that sell this product in Utah?
It is between \(\$4.15\) and \(\$4.31\).
It is either less than \(\$4.15\) or greater than \(\$4.31\).
It is less than \(\$4.15\).
It is greater than \(\$4.31\).
1. TRANSLATE the problem information
- Given information:
- Sample mean estimate: \(\$4.23\)
- Margin of error: \(\$0.08\)
- Need plausible values for true population mean
- What this tells us: We have a point estimate with associated uncertainty
2. INFER the approach
- The margin of error creates a confidence interval around our estimate
- Plausible values fall within this interval: estimate ± margin of error
- We need to calculate both endpoints of this range
3. SIMPLIFY to find the confidence interval
- Lower bound: \(\$4.23 - \$0.08 = \$4.15\)
- Upper bound: \(\$4.23 + \$0.08 = \$4.31\)
- Plausible range: \(\$4.15\) to \(\$4.31\)
Answer: A. It is between \(\$4.15\) and \(\$4.31\).
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students may misunderstand what "plausible" means in statistical context. They might think the margin of error represents values that are NOT plausible, interpreting it as the range outside which the true mean falls.
This backward reasoning leads them to select Choice B (either less than \(\$4.15\) or greater than \(\$4.31\)) - the exact opposite of the correct interpretation.
Second Most Common Error:
Poor TRANSLATE reasoning: Students may correctly understand confidence intervals but make arithmetic errors when calculating \(\$4.23 \pm \$0.08\). Common mistakes include adding when they should subtract, or vice versa.
These calculation errors cause confusion about which endpoints belong to the interval, leading to guessing among choices C or D.
The Bottom Line:
This problem tests statistical reasoning more than mathematical computation. Success depends on understanding that margin of error creates a range OF plausible values, not a range OUTSIDE of which values are implausible.
It is between \(\$4.15\) and \(\$4.31\).
It is either less than \(\$4.15\) or greater than \(\$4.31\).
It is less than \(\$4.15\).
It is greater than \(\$4.31\).