Problem

Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence interval of $(1.2,3.0)$ when estimating the mean height (in centimeters) of a sample of seedlings. The estimated margin of error is

Solution

Step 1 :The confidence interval given by the biologist is \((1.2, 3.0)\).

Step 2 :The sample mean is the midpoint of the confidence interval. It can be calculated as \((1.2 + 3.0) / 2 = 2.1\).

Step 3 :The margin of error is the difference between the upper limit of the confidence interval and the sample mean, or the sample mean minus the lower limit of the confidence interval. It can be calculated as \(3.0 - 2.1 = 0.9\) or \(2.1 - 1.2 = 0.9\).

Step 4 :Final Answer: The sample mean is \(\boxed{2.1}\) and the estimated margin of error is \(\boxed{0.9}\).

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Source: https://solvelyapp.com/problems/19208/

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