A machine fills bags with approximately ounces of cranberries. To test the accuracy of the filling process, bags of cranberries were selected at random and weighed. Based on the sample, it is estimated that the average weight of all bags of cranberries filled by the machine in an -hour period is ounces, with an associated margin of error of ounce. Which of the following is the best interpretation of this estimate?
Explanation
Context: From a random sample of bags, the average weight of all bags filled in an -hour period is estimated to be ounces with a margin of error of ounce. We must pick the best interpretation of that estimate.
Answer: A) Plausible values for the average weight of all bags of cranberries filled by the machine are between ounces and ounces.
Why: A margin of error builds an interval around the sample estimate: and . So plausible values for the true average weight of all bags run from ounces to ounces.
Traps:
- B) Describes the values outside the interval; the margin of error marks the interval around as plausible, not its complement.
- C) A margin of error never supports a one-sided claim; nothing here shows the true average exceeds ounces.
- D) Same flaw in the other direction; the estimate places the average inside an interval rather than asserting it is below ounces.