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

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 $dollar sign 4.23$ , with an associated margin of error of $dollar sign 0.08$ . 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 $dollar sign 4.15$ and $dollar sign 4.31$ .

It is either less than $dollar sign 4.15$ or greater than $dollar sign 4.31$ .

It is less than $dollar sign 4.15$ .

It is greater than $dollar sign 4.31$ .

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Explanation

Choice A is correct. It's given that the mean price of a carton of grape tomatoes in Utah was estimated to be $dollar sign 4.23$ , with an associated margin of error of $dollar sign 0.08$ . It follows that plausible values for this mean price are between $dollar sign 4.23 minus dollar sign 0.08$ and $dollar sign 4.23 plus dollar sign 0.08$ . Therefore, it's plausible that the mean price of a carton of grape tomatoes for all locations that sell this product in Utah is between $dollar sign 4.15$ and $dollar sign 4.31$ .

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.