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Problem-Solving and Data Analysis / Inference from sample statistics and margin of error Difficulty: Medium

A company fills boxes with approximately $23$ pounds of oranges. To test the accuracy of the filling process, $344$ boxes of oranges were selected at random and weighed. Based on the sample, it is estimated that the average weight of all boxes of oranges filled by the company in an $8$ -hour period is $23.1$ pounds, with an associated margin of error of $0.19$ pounds. Which of the following is the best interpretation of this estimate?

Plausible values for the average weight of all boxes of oranges filled by the company are between $22.91$ pounds and $23.29$ pounds.

Plausible values for the average weight of all boxes of oranges filled by the company are less than $22.91$ pounds or greater than $23.29$ pounds.

The average weight of all boxes of oranges filled by the company is less than $23.01$ pounds.

The average weight of all boxes of oranges filled by the company is greater than $23.01$ pounds.

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Explanation

Choice A is correct. It's given that the estimate for the average weight of all boxes of oranges filled by the company in an $8$ -hour period is $23.1$ pounds, with an associated margin of error of $0.19$ pounds. It follows that plausible values for this average weight are between $23.1 minus 0.19$ pounds and $23.1 plus 0.19$ pounds. Therefore, plausible values for the average weight of all boxes of oranges filled by the company are between $22.91$ pounds and $23.29$ pounds.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.