Question

use the confidence interval to find the estimated margin of error. then find the sample mean. a biologist reports a confidence interval of (4.5,4.9) when estimating the mean height (in centimeters) of a sample of seedlings. the estimated margin of error is

Explanation:

Step1: Recall the formula for the margin of error

The confidence interval is given by \(\bar{x}-E\) (lower bound) and \(\bar{x} + E\) (upper bound), where \(\bar{x}\) is the sample mean and \(E\) is the margin of error. The formula for the margin of error \(E=\frac{\text{upper bound}-\text{lower bound}}{2}\).

Step2: Calculate the margin of error

Given the lower bound \(L = 4.5\) and the upper bound \(U=4.9\).

$$ E=\frac{U - L}{2}=\frac{4.9-4.5}{2} $$

$$ E=\frac{0.4}{2}=0.2 $$

Answer:

\(0.2\)