Posts Tagged ‘estimated margin of error’

Use the confidence interval to find the estimated margin of error. Then find the sample mean.

Use the confidence interval to find the estimated margin of error. Then find the sample mean.

A biologist reports  a confidence interval of (3.8, 6.4) when estimating the mean height ( in centimeters) of a sample of seedlings.

Solution:-

The  confidence interval is \overline{x}\pm E where \overline{x} is the sample mean and E is the margin of error.

Divide the width of the confidence interval by 2 to find the margin of error.

\frac{6.4-3.8}{2}=1.3

Therefore, the margin of error is 1.3

The sample mean overlibe{1.3} is the middle of the confidence interval. To find the sample mean, either add the margin of error to the left endpoint or subtract the margin of error from the right endpoint. In this problem, add the margin of error to the left endpoint.

3.8 + 1.3 = 5.1

Therefore , the sample mean is 5.1.