Use the confidence interval to find the estimated margin oferror. Then find the

Question

Use the confidence interval to find the estimated margin oferror. Then find the sample mean. A bilogist reports a confidence interval of (2.0, 3.4) whenestimating the mean height (in centimeters) of a sampleseedlings. The estimated margin of error is ____. The sample mean is ____. Use the confidence interval to find the estimated margin oferror. Then find the sample mean. A bilogist reports a confidence interval of (2.0, 3.4) whenestimating the mean height (in centimeters) of a sampleseedlings. The estimated margin of error is ____. The sample mean is ____.

Explanation / Answer

A confidence interval is given by: sample mean ±margin of error. Hence the total size of the confidence interval is twice the marginof error. So to find the margin of error we simply need to halvethe confidence interval. 3.4 - 2.0 = 1.4 1.4 /2 = 0.7 Hence the margin of error is 0.7. The sample mean is right in the middle of the confidence interval.Hence we can add the margin of error to the lower bound of theconfidence interval, or take it away from the upper bound. (Bydefinition, they will both give the same result.) 2.0 + 0.7 = 2.7. Hence the sample mean is 2.7. (Check: 3.4 - 0.7 = 2.7. So everything works out and we have notmade any mistakes anywhere.)

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