Problem-Solving and Data AnalysisVery hardInterpreting a mean with a margin of error
Problem-Solving and Data Analysis practice question
A random sample of a town's households has a mean weekly grocery spend of 120 dollars, with a margin of error of 6 dollars at the 95 percent confidence level. Which of the following statements is correct?
- A. It is plausible that the mean weekly grocery spend of all the town's households is between 114 and 126 dollars.Correct
- B. 95 percent of the town's households spend between 114 and 126 dollars a week.
- C. The sample's mean is between 114 and 126 dollars.
- D. The mean for all households is exactly 120 dollars.
Answer: A. It is plausible that the mean weekly grocery spend of all the town's households is between 114 and 126 dollars.
The margin of error is about the population mean, not about individual households.
Why the other answers are wrong
- B. 95 percent of the town's households spend between 114 and 126 dollars a week.
- The interval is for the mean, not for the spread of households.
- C. The sample's mean is between 114 and 126 dollars.
- The sample mean is exactly 120.
- D. The mean for all households is exactly 120 dollars.
- A sample estimates; it does not pin the mean exactly.
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