Question

use the confidence interval to find the estimated margin of error. then find the sample mean. a biologist reports a confidence interval of (2.7,3.5) when estimating the mean height (in centimeters) of a sample of seedlings. the estimated margin of error is

Explanation:

Step1: Recall margin - of - error formula

The margin of error $E$ for a confidence interval $(a,b)$ is given by $E=\frac{b - a}{2}$. Here, $a = 2.7$ and $b = 3.5$.

Step2: Calculate the margin of error

$E=\frac{3.5-2.7}{2}=\frac{0.8}{2}=0.4$

Step3: Recall sample - mean formula

The sample mean $\bar{x}$ for a confidence interval $(a,b)$ is given by $\bar{x}=\frac{a + b}{2}$.

Step4: Calculate the sample mean

$\bar{x}=\frac{2.7+3.5}{2}=\frac{6.2}{2}=3.1$

Answer:

The estimated margin of error is $0.4$. The sample mean is $3.1$.