Question

If the margin of error in an estimate for the mean weight of a shipment is + or -2 pounds at a confidence level of 95 percent, what will be the margin of error at a confidence level of 98 percent? Be sure to show how you arrived at your answer.

Answer 1

The margin of error is found from:
\[\large M.E.=z.\sigma_{\bar{x}}\]
and is the distance from x-bar to the end of the confidence interval (C.I).
For a 95% C.I. z = 1.96.
For a 98% C.I. z = 2.33.
Therefore the margin of error at a 98% C.I. is given by:
\[\large \frac{2}{1.96}\times 2.33=\pm2.38\ pounds\]