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

A company designs and makes handbags. To estimate the mean weight of the handbags made by the company on a particular day, a sample of the handbags made by the company on that day was selected at random. Based on the sample, it is estimated that the mean weight of all handbags made by the company on that day is $27.8 ounces left parenthesis oz right parenthesis$ , with an associated margin of error of $0.02 oz$ . Based on this estimate and associated margin of error, which of the following is the most plausible conclusion?

The mean weight of all handbags made by the company on that day is between $27.78 oz$ and $27.82 oz$ .

The actual weights of all handbags made by the company on that day are between $27.78 oz$ and $27.82 oz$ .

The actual weights of all handbags from the sample are between $27.78 oz$ and $27.82 oz$ .

The mean weight of all handbags made by the company on that day is $27.8 oz$ .

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Explanation

Choice A is correct. It's given that the estimated mean weight of all handbags made by the company on a particular day is $27.8 oz$ , with an associated margin of error of $0.02 oz$ . It follows that plausible values for the mean weight are between $left parenthesis 27.8 minus 0.02 right parenthesis oz$ and $left parenthesis 27.8 plus 0.02 right parenthesis oz$ . Therefore, the most plausible conclusion is that the mean weight of all handbags made by the company on that day is between $27.78 oz$ and $27.82 oz$ .

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.